Second-order Born approximation for the scattering phase shifts: Application to the Friedel sum rule
NASA Astrophysics Data System (ADS)
Nersisyan, Hrachya B.; Fernández-Varea, José M.
2013-09-01
Screening effects are important to understand various aspects of ion-solid interactions and, in particular, play a crucial role in the stopping of ions in solids. In this paper the phase shifts and scattering amplitudes for the quantum-mechanical elastic scattering within up to the second-order Born (B2) approximation are revisited for an arbitrary spherically-symmetric electron-ion interaction potential. The B2 phase shifts and scattering amplitudes are then used to derive the Friedel sum rule (FSR) involving the second-order Born corrections. This results in a simple equation for the B2 perturbative screening parameter of an impurity ion immersed in a fully degenerate electron gas which, as expected, turns out to depend on the ion atomic number Z1 unlike the first-order Born (B1) screening parameter reported earlier by some authors. Furthermore, our analytical results for the Yukawa, hydrogenic, Hulthén, and Mensing potentials are compared, for both positive and negative ions and a wide range of one-electron radii, to the exact screening parameters calculated self-consistently by imposing the FSR requirement. It is shown that the B2 screening parameters agree excellently with the exact values at large and moderate densities of the degenerate electron gas, while at lower densities they progressively deviate from the exact numerical solutions but are nevertheless more accurate than the prediction of the B1 approximation. In addition, a simple Padé approximant to the Born series has been developed that improves the performance of the perturbative FSR for any negative ion as well as for Z1=+1.
NASA Astrophysics Data System (ADS)
Spinrath, Martin
2016-06-01
There is a wide class of models which give a dynamical description of the origin of flavor in terms of spontaneous symmetry breaking of an underlying symmetry. Many of these models exhibit sum rules which relate on the one hand mixing angles and the Dirac CP phase with each other and/or on the other hand neutrino masses and Majorana phases with each other. We will briefly sketch how this happens and discuss briefly the impact of renormalization group corrections to the mass sum rules.
NASA Astrophysics Data System (ADS)
Spinrath, Martin
There is a wide class of models which give a dynamical description of the origin of avor in terms of spontaneous symmetry breaking of an underlying symmetry. Many of these models exhibit sum rules which relate on the one hand mixing angles and the Dirac CP phase with each other and/or on the other hand neutrino masses and Majorana phases with each other. We will briey sketch how this happens and discuss briey the impact of renormalization group corrections to the mass sum rules.
``Robinson's sum rule'' revisited
NASA Astrophysics Data System (ADS)
Orlov, Yuri F.
2010-02-01
This discussion revisits two articles on synchrotron radiation damping published in 1958, one by this author and Evgeny K. Tarasov [Zh. Eksp. Teor. Fiz. 34, 651 (1958)ZETFA70044-4510; Sov. Phys. JETP 34, 449 (1958)SPHJAR0038-5646], and one by Kenneth W. Robinson [Phys. Rev. 111, 373 (1958)PHRVAO0031-899X10.1103/PhysRev.111.373]. The latter is the source of what is known as “Robinson’s sum rule.” Both present the familiar rule, but with very different proofs and calculations of concrete damping decrements. Comparative analysis of these differences reveals serious flaws in Robinson’s proof and calculations.
Fluctuations in classical sum rules
NASA Astrophysics Data System (ADS)
Elton, John R.; Lakshminarayan, Arul; Tomsovic, Steven
2010-10-01
Classical sum rules arise in a wide variety of physical contexts. Asymptotic expressions have been derived for many of these sum rules in the limit of long orbital period (or large action). Although sum-rule convergence may well be exponentially rapid for chaotic systems in a global phase-space sense with time, individual contributions to the sums may fluctuate with a width which diverges in time. Our interest is in the global convergence of sum rules as well as their local fluctuations. It turns out that a simple version of a lazy baker map gives an ideal system in which classical sum rules, their corrections, and their fluctuations can be worked out analytically. This is worked out in detail for the Hannay-Ozorio sum rule. In this particular case the rate of convergence of the sum rule is found to be governed by the Pollicott-Ruelle resonances, and both local and global boundaries for which the sum rule may converge are given. In addition, the width of the fluctuations is considered and worked out analytically, and it is shown to have an interesting dependence on the location of the region over which the sum rule is applied. It is also found that as the region of application is decreased in size the fluctuations grow. This suggests a way of controlling the length scale of the fluctuations by considering a time dependent phase-space volume, which for the lazy baker map decreases exponentially rapidly with time.
The Orbital Angular Momentum Sum Rule
NASA Astrophysics Data System (ADS)
Aslan, Fatma; Burkardt, Matthias
2015-10-01
As an alternative to the Ji sum rule for the quark angular momentum, a sum rule for the quark orbital angular momentum, based on a twist-3 generalized parton distribution, has been suggested. We study the validity of this sum rule in the context of scalar Yukawa interactions as well as in QED for an electron.
Relativistic corrections to a generalized sum rule
NASA Astrophysics Data System (ADS)
Sinky, H.; Leung, P. T.
2006-09-01
Relativistic corrections to a previously established generalized sum rule are obtained using the Foldy-Wouthysen transformation. This sum rule derived previously by Wang [Phys. Rev. A 60, 262 (1999)] for a nonrelativistic system contains both the well-known Thomas-Reiche-Kuhn and Bethe sum rules, for which relativistic corrections have been obtained in the literature. Our results for the generalized formula will be applied to recover several results obtained previously in the literature, as well as to another sum rule whose relativistic corrections will be obtained.
S=+1 pentaquarks in QCD sum rules
NASA Astrophysics Data System (ADS)
Gubler, Philipp; Jido, Daisuke; Kojo, Toru; Nishikawa, Tetsuo; Oka, Makoto
2009-10-01
The QCD sum rule technique is employed to investigate pentaquark states with strangeness S = +1 and IJ^π = 012^±,112^±,032^ ±,132^±. Throughout the calculation, we emphasize the importance of the establishment of a valid Borel window, which corresponds to a region of the Borel mass, where the operator product expansion (OPE) converges and the presumed ground state pole dominates the sum rules. Such a Borel window is achieved by constructing the sum rules from the differenece of two carefully chosen independent correlators and by calculating the OPE up to dimension 14. As a result, we conclude that the state with qauntum numbers 032^+ state appears to be the most probable candidate for the experimantally observed &+circ;(1540), while we also obtain states with 012^-,112^-,132^+ at somewhat higher mass regions. We furthermore discuss the contribution of the KN scattering states to the sum rules, and the possible influence of these states on our results.
Generalized Thomas-Reiche-Kuhn sum rule
NASA Astrophysics Data System (ADS)
Zhou, Bing-Lu; Zhu, Jiong-Ming; Yan, Zong-Chao
2006-01-01
The generalized Thomas-Reiche-Kuhn sum rule is established for any Coulombic system with arbitrary masses and charges of its constituent particles. Numerical examples are given for the hydrogen molecular ions.
Nuclear magnetic moments and related sum rules
Bentz, Wolfgang; Arima, Akito
2011-05-06
We first review the history and our present understanding of nuclear magnetic moments and Gamow-Teller transitions, with emphasis on the roles of configuration mixing and meson exchange currents. Then we discuss the renormalization of the orbital g-factor in nuclei, and its relation to the E1 sum rule for photoabsorption and the M1 sum rule for the scissors mode of deformed nuclei.
Sum rules in the oscillator radiation processes
NASA Astrophysics Data System (ADS)
Casana, R.; Flores-Hidalgo, G.; Pimentel, B. M.
2005-03-01
We consider the problem of a harmonic oscillator coupled to a scalar field in the framework of recently introduced dressed coordinates. We compute all the probabilities associated with the decay process of an excited level of the oscillator. Instead of doing direct quantum mechanical calculations we establish some sum rules from which we infer the probabilities associated to the different decay processes of the oscillator. Thus, the sum rules allows to show that the transition probabilities between excited levels follow a binomial distribution.
Predictivity of neutrino mass sum rules
NASA Astrophysics Data System (ADS)
Gehrlein, Julia; Merle, Alexander; Spinrath, Martin
2016-11-01
Correlations between light neutrino observables are arguably the strongest predictions of lepton flavor models based on (discrete) symmetries, except for the very few cases which unambiguously predict the full set of leptonic mixing angles. A subclass of these correlations is neutrino mass sum rules, which connect the three (complex) light neutrino mass eigenvalues among each other. This connection constrains both the light neutrino mass scale and the Majorana phases, so that mass sum rules generically lead to a nonzero value of the lightest neutrino mass and to distinct predictions for the effective mass probed in neutrinoless double beta decay. However, in nearly all cases known, the neutrino mass sum rules are not exact and receive corrections from various sources. We introduce a formalism to handle these corrections perturbatively in a model-independent manner, which overcomes issues present in earlier approaches. Our ansatz allows us to quantify the modification of the predictions derived from neutrino mass sum rules. We show that, in most cases, the predictions are fairly stable: while small quantitative changes can appear, they are generally rather mild. We therefore establish the predictivity of neutrino mass sum rules on a level far more general than previously known.
S=+1 pentaquarks in QCD sum rules
NASA Astrophysics Data System (ADS)
Gubler, Philipp; Jido, Daisuke; Kojo, Toru; Nishikawa, Tetsuo; Oka, Makoto
2010-04-01
We study pentaquark states with strangeness S=+1 and IJ=01,11,03,13 within the QCD sum rule technique. In order to obtain reliable results with this method, it is indispensable to establish a valid Borel window, where the operator product expansion (OPE) converges and the presumed ground state pole dominates the sum rules. By constructing the sum rules from the difference of two carefully chosen independent correlators and calculating the OPE up to dimension 14, such a Borel window can be established. This then leads to our main conclusion that the state with qantum numbers 03 appears to be the most probable candidate for the experimentally observed Θ(1540). Furthermore, states with 01,11,13 are also obtained at slightly higher mass regions.
Systematics of strength function sum rules
NASA Astrophysics Data System (ADS)
Johnson, Calvin W.
2015-11-01
Sum rules provide useful insights into transition strength functions and are often expressed as expectation values of an operator. In this letter I demonstrate that non-energy-weighted transition sum rules have strong secular dependences on the energy of the initial state. Such non-trivial systematics have consequences: the simplification suggested by the generalized Brink-Axel hypothesis, for example, does not hold for most cases, though it weakly holds in at least some cases for electric dipole transitions. Furthermore, I show the systematics can be understood through spectral distribution theory, calculated via traces of operators and of products of operators. Seen through this lens, violation of the generalized Brink-Axel hypothesis is unsurprising: one expects sum rules to evolve with excitation energy. Furthermore, to lowest order the slope of the secular evolution can be traced to a component of the Hamiltonian being positive (repulsive) or negative (attractive).
NASA Astrophysics Data System (ADS)
Ziesche, P.; Pernal, K.; Tasnádi, F.
2003-09-01
Recently, new sum rules for the scattering phase shifts of the pair-density geminals (being 2-body-wave functions which parametrize the pair density together with an appropriately chosen occupancy) have been derived from the normalization of the pair density [P. Ziesche, Phys. Rev. B 67, 233102 (2003)]. Here, we present a generalization of these sum rules, which allows one in principle to calculate the momentum distribution from these geminals and their phase shifts. These contraction sum rules contain the afore mentioned (Friedel-like) normalization sum rules as special cases.
Pentaquarks in QCD Sum Rule Approach
Rodrigues da Silva, R.; Matheus, R.D.; Navarra, F.S.; Nielsen, M.
2004-12-02
We estimate the mass of recently observed pentaquak staes {xi}- (1862) and {theta}+(1540) using two kinds of interpolating fields, containing two highly correlated diquarks, in the QCD sum rule approach. We obtained good agreement with the experimental value, using standard continuum threshold.
S=+1 pentaquarks in QCD sum rules
Kojo, T.; Gubler, P.; Jido, D.; Nishikawa, T.; Oka, M.
2010-04-01
The QCD sum rule technique is employed to investigate pentaquark states with strangeness S = +1 and IJ{sup {pi}} = 0 1/2{sup {+-}}, 1 1/2{sup {+-}}, 0 3/2{sup {+-}}, 1 3/2{sup {+-}}. Throughout the calculation, we emphasize the importance of the establishment of a valid Borel window, which corresponds to a region of the Borel mass, where the operator product expansion (OPE) converges and the presumed ground state pole dominates the sum rules. Such a Borel window is achieved by constructing the sum rules from the differenece of two carefully chosen independent correlators and by calculating the OPE up to dimension 14. As a result, we conclude that the state with qauntum numbers 0 3/2{sup +} state appears to be the most probable candidate for the experimentally observed {Theta}{sup +}(1540), while we also obtain states with 0 1/2{sup -}, 1 1/2{sup -}, 1 3/2{sup +} at somewhat higher mass regions. We furthermore discuss the contribution of the KN scattering states to the sum rules, and the possible influence of these states on our results.
Systematics of strength function sum rules
Johnson, Calvin W.
2015-08-28
Sum rules provide useful insights into transition strength functions and are often expressed as expectation values of an operator. In this letter I demonstrate that non-energy-weighted transition sum rules have strong secular dependences on the energy of the initial state. Such non-trivial systematics have consequences: the simplification suggested by the generalized Brink–Axel hypothesis, for example, does not hold for most cases, though it weakly holds in at least some cases for electric dipole transitions. Furthermore, I show the systematics can be understood through spectral distribution theory, calculated via traces of operators and of products of operators. Seen through this lens,more » violation of the generalized Brink–Axel hypothesis is unsurprising: one expectssum rules to evolve with excitation energy. Moreover, to lowest order the slope of the secular evolution can be traced to a component of the Hamiltonian being positive (repulsive) or negative (attractive).« less
Optical Thomas-Reiche-Kuhn sum rules.
Barnett, Stephen M; Loudon, Rodney
2012-01-06
The Thomas-Reiche-Kuhn sum rule is a fundamental consequence of the position-momentum commutation relation for an atomic electron and it provides an important constraint on the transition matrix elements for an atom. Analogously, the commutation relations for the electromagnetic field operators in a magnetodielectric medium constrain the properties of the dispersion relations for the medium through four sum rules for the allowed phase and group velocities for polaritons propagating through the medium. These rules apply to all bulk media including the metamaterials designed to provide negative refractive indices. An immediate consequence of this is that it is not possible to construct a medium in which all the polariton modes for a given wavelength lie in the negative-index region.
Optical Thomas-Reiche-Kuhn Sum Rules
NASA Astrophysics Data System (ADS)
Barnett, Stephen M.; Loudon, Rodney
2012-01-01
The Thomas-Reiche-Kuhn sum rule is a fundamental consequence of the position-momentum commutation relation for an atomic electron and it provides an important constraint on the transition matrix elements for an atom. Analogously, the commutation relations for the electromagnetic field operators in a magnetodielectric medium constrain the properties of the dispersion relations for the medium through four sum rules for the allowed phase and group velocities for polaritons propagating through the medium. These rules apply to all bulk media including the metamaterials designed to provide negative refractive indices. An immediate consequence of this is that it is not possible to construct a medium in which all the polariton modes for a given wavelength lie in the negative-index region.
Systematics of strength function sum rules
Johnson, Calvin W.
2015-08-28
Sum rules provide useful insights into transition strength functions and are often expressed as expectation values of an operator. In this letter I demonstrate that non-energy-weighted transition sum rules have strong secular dependences on the energy of the initial state. Such non-trivial systematics have consequences: the simplification suggested by the generalized Brink–Axel hypothesis, for example, does not hold for most cases, though it weakly holds in at least some cases for electric dipole transitions. Furthermore, I show the systematics can be understood through spectral distribution theory, calculated via traces of operators and of products of operators. Seen through this lens, violation of the generalized Brink–Axel hypothesis is unsurprising: one expectssum rules to evolve with excitation energy. Moreover, to lowest order the slope of the secular evolution can be traced to a component of the Hamiltonian being positive (repulsive) or negative (attractive).
New QCD sum rules based on canonical commutation relations
NASA Astrophysics Data System (ADS)
Hayata, Tomoya
2012-04-01
New derivation of QCD sum rules by canonical commutators is developed. It is the simple and straightforward generalization of Thomas-Reiche-Kuhn sum rule on the basis of Kugo-Ojima operator formalism of a non-abelian gauge theory and a suitable subtraction of UV divergences. By applying the method to the vector and axial vector current in QCD, the exact Weinberg’s sum rules are examined. Vector current sum rules and new fractional power sum rules are also discussed.
Advances in QCD sum-rule calculations
Melikhov, Dmitri
2016-01-22
We review the recent progress in the applications of QCD sum rules to hadron properties with the emphasis on the following selected problems: (i) development of new algorithms for the extraction of ground-state parameters from two-point correlators; (ii) form factors at large momentum transfers from three-point vacuum correlation functions: (iii) properties of exotic tetraquark hadrons from correlation functions of four-quark currents.
Orlov, Tarasov, and the Robinson Sum Rule
Talman, Richard; Chao, Alexander W.; /SLAC
2011-12-01
A paper proving a result now commonly known as 'Robinson sum rule' was published by Orlov and Tarasov [J. Exp. Theor. Phys. 34 651 (1958) Sov. Phys. JETP 34 339 (1958)] at about the same time that Robinson himself published the result [Phys. Rev. 111 373 (1958)]. We assigned ourselves the task of reviewing this work, as narrowly as possible, in hopes of understanding how it should be considered in view of the existing attribution. The chronology of the work is reviewed and the degree to which the two works were independent and have qualitatively different content is considered.
A cluster version of the GGT sum rule
NASA Astrophysics Data System (ADS)
Hencken, Kai; Baur, Gerhard; Trautmann, Dirk
2004-03-01
We discuss the derivation of a "cluster sum rule" from the Gellmann-Goldberger-Thirring (GGT) sum rule as an alternative to the Thomas-Reiche-Kuhn (TRK) sum rule, which was used as the basis up to now. We compare differences in the assumptions and approximations. Some applications of the sum rule for halo nuclei, as well as, nuclei with a pronounced cluster structure are discussed.
QCD Sum Rules Study of X(4350)
NASA Astrophysics Data System (ADS)
Mo, Zeng; Cui, Chun-Yu; Liu, Yong-Lu; Huang, Ming-Qiu
2014-04-01
The QCD sum rule approach is used to analyze the nature of the recently observed new resonance X(4350), which is assumed to be a diquark-antidiquark state [cs][bar cbar s] with JPC = 1-+. The interpolating current representing this state is proposed. In the calculation, contributions of operators up to dimension six are included in the operator product expansion (OPE), as well as terms which are linear in the strange quark mass ms. We find m1-+ = (4.82 ± 0.19) GeV, which is not compatible with the X(4350) structure as a 1-+ tetraquark state. Finally, we also discuss the difference of a four-quark state's mass whether the state's interpolating current has a definite charge conjugation.
Sum Rule for a Schiff-Like Dipole Moment
NASA Astrophysics Data System (ADS)
Raduta, A. A.; Budaca, R.
The energy-weighted sum rule for an electric dipole transition operator of a Schiff type differs from the Thomas-Reiche-Kuhn (TRK) sum rule by several corrective terms which depend on the number of system components, N. For illustration the formalism was applied to the case of Na clusters. One concludes that the random phase approximation (RPA) results for Na clusters obey the modified TRK sum rule.
Tuning sum rules with window functions for optical constant evaluation
NASA Astrophysics Data System (ADS)
Rodríguez-de Marcos, Luis V.; Méndez, José A.; Larruquert, Juan I.
2016-07-01
Sum rules are a useful tool to evaluate the global consistency of a set of optical constants. We present a procedure to spectrally tune sum rules to evaluate the local consistency of optical constants. It enables enhancing the weight of a desired spectral range within the sum-rule integral. The procedure consists in multiplying the complex refractive index with an adapted function, which is named window function. Window functions are constructed through integration of Lorentz oscillators. The asymptotic decay of these window functions enables the derivation of a multiplicity of sum rules akin to the inertial sum rule, along with one modified version of f-sum rule. This multiplicity of sum rules combined with the free selection of the photon energy range provides a double way to tune the spectral contribution within the sum rule. Window functions were applied to reported data of SrF2 and of Al films in order to check data consistency over the spectrum. The use of window functions shows that the optical constants of SrF2 are consistent in a broad spectrum. Regarding Al, some spectral ranges are seen to present a lower consistency, even though the standard sum rules with no window function did not detect inconsistencies. Hence window functions are expected to be a helpful tool to evaluate the local consistency of optical constants.
Charmonium sum rules applied to a holographic model
Hohler, Paul M.
2011-01-15
The heavy-quark QCD sum rules are applied to a model of charmonium based upon the gauge/gravity duality. We find that there is strong agreement between the moments of the polarization function calculated from the holographic model and the experimental data suggesting that the model is consistent with the heavy-quark QCD sum rules at zero temperature.
Second sum rule for the hot plasma permittivity
Bobrov, V. B.; Mendeleyev, V. Ya.; Skovorod'ko, S. N.; Trigger, S. A.
2011-02-15
Based on linear response theory, Kramers-Kronig relations, and diagram techniques of perturbation theory, it is shown that the second sum rule is satisfied for hot plasma permittivity. An explicit analytical expression for the second sum rule in the limit of weak nonideality is derived.
Range of validity for perturbative treatments of relativistic sum rules
NASA Astrophysics Data System (ADS)
Cohen, Scott M.
2003-10-01
The range of validity of perturbative calculations of relativistic sum rules is investigated by calculating the second-order relativistic corrections to the Bethe sum rule and its small momentum limit, the Thomas-Reiche-Kuhn (TRK) sum rule. For the TRK sum rule and atomic systems, the second-order correction is found to be less than 0.5% up to about Z=70. The total relativistic corrections should then be accurate at least through this range of Z, and probably beyond this range if the second-order terms are included. For Rn (Z=86), however, the second-order corrections are nearly 1%. The total corrections to the Bethe sum rule are largest at small momentum, never being significantly larger than the corresponding corrections to the TRK sum rule. The first-order corrections to the Bethe sum rule also give better than 0.5% accuracy for Z<70, and inclusion of the second-order corrections should extend this range, as well.
Shear spectral sum rule in a nonconformal gravity dual
Springer, Todd; Gale, Charles; Jeon, Sangyong; Lee, Su Houng
2010-11-15
A sum rule which relates a stress-energy tensor correlator to thermodynamic functions is examined within the context of a simple nonconformal gravity dual. Such a sum rule was previously derived using AdS/CFT for conformal N=4 supersymmetric Yang-Mills theory, but we show that it does not generalize to the nonconformal theory under consideration. We provide a generalized sum rule and numerically verify its validity. A useful by-product of the calculation is the computation of the spectral density in a strongly coupled nonconformal theory. Qualitative features of the spectral densities and implications for lattice measurements of transport coefficients are discussed.
The moment sum-rules for ionic liquids at criticality
NASA Astrophysics Data System (ADS)
Fantoni, Riccardo
2017-07-01
We discuss the first three well known moment charge-charge sum-rules for a general ionic liquid. For the special symmetric case of the Restricted Primitive Model, Das, Kim, and Fisher (2011) has recently discovered, through Monte Carlo simulations, that the Stillinger-Lovett or second-moment sum-rule fails at criticality. We critically discuss a possible explanation for this unexpected behavior. On the other hand the fourth-moment sum-rule turns out to be able to account for the results of the simulations at criticality.
Quark mixing sum rules and the right unitarity triangle
Antusch, Stefan; Spinrath, Martin; King, Stephen F.; Malinsky, Michal
2010-02-01
In analogy with the recently proposed lepton mixing sum rules, we derive quark mixing sum rules for the case of hierarchical quark mass matrices with 1-3 texture zeros, in which the separate up and down-type 1-3 mixing angles are approximately zero, and V{sub ub} is generated from V{sub cb} as a result of 1-2 up-type quark mixing. Using the sum rules, we discuss the phenomenological viability of such textures, including up to four texture zeros, and show how the right-angled unitarity triangle, i.e., {alpha}{approx_equal}90 deg., can be accounted for by a remarkably simple scheme involving real mass matrices apart from a single element being purely imaginary. In the framework of grand unified theories, we show how the quark and lepton mixing sum rules may combine to yield an accurate prediction for the reactor angle.
Compton Scattering and Photo-absorption Sum Rules on Nuclei
NASA Astrophysics Data System (ADS)
Gorshteyn, Mikhail; Hobbs, Timothy; Londergan, J. Timothy; Szczepaniak, Adam P.
2012-03-01
We revisit the photo-absorption sum rule for real Compton scattering from the proton and from nuclear targets. In analogy with the Thomas-Reiche-Kuhn sum rule appropriate at low energies, we propose a new ``constituent quark model'' sum rule that relates the integrated strength of hadronic resonances to the scattering amplitude on constituent quarks. We study the constituent quark model sum rule for several nuclear targets. In addition we extract the J=0 pole contribution for both proton and nuclei. Using the modern high energy proton data we find that the J=0 pole contribution differs significantly from the Thomson term, in contrast with the original findings by Damashek and Gilman. We discuss phenomenological implications of this new result.
Compton scattering from nuclei and photo-absorption sum rules
NASA Astrophysics Data System (ADS)
Gorchtein, Mikhail; Hobbs, Timothy; Londergan, J. Timothy; Szczepaniak, Adam P.
2011-12-01
We revisit the photo-absorption sum rule for real Compton scattering from the proton and from nuclear targets. In analogy with the Thomas-Reiche-Kuhn sum rule appropriate at low energies, we propose a new “constituent quark model” sum rule that relates the integrated strength of hadronic resonances to the scattering amplitude on constituent quarks. We study the constituent quark model sum rule for several nuclear targets. In addition, we extract the α=0 pole contribution for both proton and nuclei. Using the modern high-energy proton data, we find that the α=0 pole contribution differs significantly from the Thomson term, in contrast with the original findings by Damashek and Gilman.
Charm and bottom hadronic form factors with QCD sum rules
Bracco, M. E.; Rodrigues, B. O.; Cerqueira, A. Jr.
2013-03-25
We present a brief review of some calculations of form factors and coupling constants in vertices with charm and bottom mesons in the framework of QCD sum rules. We first discuss the motivation for this work, describing possible applications of these form factors to charm and bottom decays processes. We first make a summarize of the QCD sum rules method. We give special attention to the uncertainties of the method introducing by the intrinsic variation of the parameters. Finally we conclude.
A novel look at the Michael lattice sum rules
NASA Astrophysics Data System (ADS)
Rothe, Heinz J.
1995-02-01
We reconsider the derivation of the Michael lattice sum rules, which relate the energy and action stored in a flux tube of a quark-antiquark pair to the static interquark potential, and show that they require essential corrections. We then find, using the coupling constant sum rule of Karsch, that the total Minkowski field energy does not match the interquark potential, if one follows conventional notions. The implications of this result are discussed.
The beauty of impurities: Two revivals of Friedel's virtual bound-state concept
NASA Astrophysics Data System (ADS)
Georges, Antoine
2016-03-01
Jacques Friedel pioneered the theoretical study of impurities and magnetic impurities in metals. He discovered Friedel oscillations, introduced the concept of virtual bound-state, and demonstrated that the charge on the impurity is related to the scattering phase-shift at the Fermi level (Friedel sum-rule). After a brief review of some of these concepts, I describe how they proved useful in two new contexts. The first one concerns the Coulomb blockade in quantum dots, and its suppression by the Kondo effect. The second one is the dynamical mean-field theory of strong electronic correlations.
Chiral corrections to the Adler-Weisberger sum rule
NASA Astrophysics Data System (ADS)
Beane, Silas R.; Klco, Natalie
2016-12-01
The Adler-Weisberger sum rule for the nucleon axial-vector charge, gA , offers a unique signature of chiral symmetry and its breaking in QCD. Its derivation relies on both algebraic aspects of chiral symmetry, which guarantee the convergence of the sum rule, and dynamical aspects of chiral symmetry breaking—as exploited using chiral perturbation theory—which allow the rigorous inclusion of explicit chiral symmetry breaking effects due to light-quark masses. The original derivations obtained the sum rule in the chiral limit and, without the benefit of chiral perturbation theory, made various attempts at extrapolating to nonvanishing pion masses. In this paper, the leading, universal, chiral corrections to the chiral-limit sum rule are obtained. Using PDG data, a recent parametrization of the pion-nucleon total cross sections in the resonance region given by the SAID group, as well as recent Roy-Steiner equation determinations of subthreshold amplitudes, threshold parameters, and correlated low-energy constants, the Adler-Weisberger sum rule is confronted with experimental data. With uncertainty estimates associated with the cross-section parametrization, the Goldberger-Treimann discrepancy, and the truncation of the sum rule at O (Mπ4) in the chiral expansion, this work finds gA=1.248 ±0.010 ±0.007 ±0.013 .
Simple and accurate sum rules for highly relativistic systems
NASA Astrophysics Data System (ADS)
Cohen, Scott M.
2005-03-01
In this paper, I consider the Bethe and Thomas-Reiche-Kuhn sum rules, which together form the foundation of Bethe's theory of energy loss from fast charged particles to matter. For nonrelativistic target systems, the use of closure leads directly to simple expressions for these quantities. In the case of relativistic systems, on the other hand, the calculation of sum rules is fraught with difficulties. Various perturbative approaches have been used over the years to obtain relativistic corrections, but these methods fail badly when the system in question is very strongly bound. Here, I present an approach that leads to relatively simple expressions yielding accurate sums, even for highly relativistic many-electron systems. I also offer an explanation for the difference between relativistic and nonrelativistic sum rules in terms of the Zitterbewegung of the electrons.
Sum Rules, Classical and Quantum - A Pedagogical Approach
NASA Astrophysics Data System (ADS)
Karstens, William; Smith, David Y.
2014-03-01
Sum rules in the form of integrals over the response of a system to an external probe provide general analytical tools for both experiment and theory. For example, the celebrated f-sum rule gives a system's plasma frequency as an integral over the optical-dipole absorption spectrum regardless of the specific spectral distribution. Moreover, this rule underlies Smakula's equation for the number density of absorbers in a sample in terms of the area under their absorption bands. Commonly such rules are derived from quantum-mechanical commutation relations, but many are fundamentally classical (independent of ℏ) and so can be derived from more transparent mechanical models. We have exploited this to illustrate the fundamental role of inertia in the case of optical sum rules. Similar considerations apply to sum rules in many other branches of physics. Thus, the ``attenuation integral theorems'' of ac circuit theory reflect the ``inertial'' effect of Lenz's Law in inductors or the potential energy ``storage'' in capacitors. These considerations are closely related to the fact that the real and imaginary parts of a response function cannot be specified independently, a result that is encapsulated in the Kramers-Kronig relations. Supported in part by the US Department of Energy, Office of Nuclear Physics under contract DE-AC02-06CH11357.
Additional corrections to the Gross-Llewellyn Smith sum rule
Londergan, J. T.; Thomas, A. W.
2010-12-01
We investigate some QCD corrections that contribute to the Gross-Llewellyn Smith sum rule but have not been included in previous analyses of it. We first review the techniques by which the xF{sub 3} structure function is extracted from combinations of neutrino and antineutrino cross sections. Next we investigate corrections to the Gross-Llewellyn Smith sum rule, with particular attention to contributions arising from strange quark distributions and from charge symmetry violating parton distributions. We find that additional corrections from strange quarks and parton charge symmetry violation are likely to have a small but potentially significant role in decreasing the current discrepancy between the experimental and theoretical estimates of the Gross-Llewellyn Smith sum rule.
Violation of an f -sum rule with generalized kinetic energy
NASA Astrophysics Data System (ADS)
Limtragool, Kridsanaphong; Phillips, Philip W.
2017-05-01
Motivated by the normal state of the cuprates in which the integrated spectral weight of the optical conductivity or optical sum increases faster than a linear function of the particle density, we derive an f -sum rule for a system in which the kinetic-energy operator in the Hamiltonian is a general function of the momentum squared. Such a kinetic energy arises in scale invariant theories and can be derived within the context of holography. Our derivation of the f -sum rule is based on the gauge couplings of a nonlocal Lagrangian in which the kinetic operator is a fractional Laplacian of order α . We find that the f -sum rule in this case deviates from the standard linear dependence on the particle density. We find two regimes. At high temperatures and low densities, the optical sum is proportional to n Tα/-1 α where T is the temperature. At low temperatures and high densities, the optical sum is proportional to n1 +2/(α -1 ) d with d being the number of spatial dimensions. The result in the low-temperature and high-density limit, when α <1 , can be used to qualitatively explain the behavior of the effective number of charge carriers in the cuprates at various doping concentrations.
Charm quark mass determined from a pair of sum rules
NASA Astrophysics Data System (ADS)
Erler, Jens; Masjuan, Pere; Spiesberger, Hubert
2016-11-01
In this paper, we present preliminary results of the determination of the charm quark mass m̂c from QCD sum rules of moments of the vector current correlator calculated in perturbative QCD at 𝒪(α̂s3). Self-consistency between two different sum rules allow to determine the continuum contribution to the moments without requiring experimental input, except for the charm resonances below the continuum threshold. The existing experimental data from the continuum region is used, then, to confront the theoretical determination and reassess the theoretic uncertainty.
D Meson Properties in Nuclear Medium from QCD Sum Rules
NASA Astrophysics Data System (ADS)
Suzuki, Kei; Gubler, Philipp; Oka, Makoto
Properties of the pseudoscalar D meson in the nuclear medium are discussed from the point of view of QCD sum rules. QCD sum rules can relate condensates in the QCD vacuum to the properties of hadrons, so that in-medium modifications of hadron spectra naively correspond to condensate modifications through nuclear matter effects. We found that the reduction of the chiral-symmetry-breaking condensates including < \\bar{q}q> leads to increasing masses of both D+ and D- mesons at finite density. Furthermore, charge-symmetry-breaking condensates cause D+-D- (particle and anti-particle) mass splitting in the nuclear medium.
Nucleon QCD sum rules in the instanton medium
Ryskin, M. G.; Drukarev, E. G. Sadovnikova, V. A.
2015-09-15
We try to find grounds for the standard nucleon QCD sum rules, based on a more detailed description of the QCD vacuum. We calculate the polarization operator of the nucleon current in the instanton medium. The medium (QCD vacuum) is assumed to be a composition of the small-size instantons and some long-wave gluon fluctuations. We solve the corresponding QCD sum rule equations and demonstrate that there is a solution with the value of the nucleon mass close to the physical one if the fraction of the small-size instantons contribution is w{sub s} ≈ 2/3.
Beauty vector meson decay constants from QCD sum rules
Lucha, Wolfgang; Melikhov, Dmitri; Simula, Silvano
2016-01-22
We present the outcomes of a very recent investigation of the decay constants of nonstrange and strange heavy-light beauty vector mesons, with special emphasis on the ratio of any such decay constant to the decay constant of the corresponding pseudoscalar meson, by means of Borel-transformed QCD sum rules. Our results suggest that both these ratios are below unity.
Spectral sum rules for conformal field theories in arbitrary dimensions
NASA Astrophysics Data System (ADS)
Chowdhury, Subham Dutta; David, Justin R.; Prakash, Shiroman
2017-07-01
We derive spectral sum rules in the shear channel for conformal field theories at finite temperature in general d ≥ 3 dimensions. The sum rules result from the OPE of the stress tensor at high frequency as well as the hydrodynamic behaviour of the theory at low frequencies. The sum rule states that a weighted integral of the spectral density over frequencies is proportional to the energy density of the theory. We show that the proportionality constant can be written in terms the Hofman-Maldacena variables t 2 , t 4 which determine the three point function of the stress tensor. For theories which admit a two derivative gravity dual this proportionality constant is given by d/2(d+1) . We then use causality constraints and obtain bounds on the sum rule which are valid in any conformal field theory. Finally we demonstrate that the high frequency behaviour of the spectral function in the vector and the tensor channel are also determined by the Hofman-Maldacena variables.
Decay Constants of Beauty Mesons from QCD Sum Rules
NASA Astrophysics Data System (ADS)
Lucha, Wolfgang; Melikhov, Dmitri; Simula, Silvano
2014-11-01
Our recently completed analysis of the decay constants of both pseudoscalar and vector beauty mesons reveals that in the bottom-quark sector two specific features of the sum-rule predictions show up: (i) For the input value of the bottom-quark mass in the M̅S̅ scheme m̅b(m̅b) ≈ 4:18 GeV; the sum-rule result fB ≈ 210-220 MeV for the B meson decay constant is substantially larger than the recent lattice-QCD finding fB ≈ 190 MeV: Requiring QCD sum rules to reproduce the lattice-QCD value of fB yields a significantly larger b-quark mass: m̅b(m̅b) = 4:247 GeV: (ii) Whereas QCD sum-rule predictions for the charmed-meson decay constants fD; fDs, fD* and fDs* are practically independent of the choice of renormalization scale, in the beauty sector the results for the decay constants—and especially for the ratio fB* / fB—prove to be very sensitive to the specific scale setting.
Beauty vector meson decay constants from QCD sum rules
NASA Astrophysics Data System (ADS)
Lucha, Wolfgang; Melikhov, Dmitri; Simula, Silvano
2016-01-01
We present the outcomes of a very recent investigation of the decay constants of nonstrange and strange heavy-light beauty vector mesons, with special emphasis on the ratio of any such decay constant to the decay constant of the corresponding pseudoscalar meson, by means of Borel-transformed QCD sum rules. Our results suggest that both these ratios are below unity.
Inequalities for frequency-moment sum rules of electron liquids
NASA Technical Reports Server (NTRS)
Iwamoto, N.
1986-01-01
The relations between the various frequency-moment sum rules of electron liquids, which include even-power moments, are systematically examined by using the Cauchy-Schwarz and Hoelder inequalities. A relation involving the isothermal sound velocity and the kinetic and potential energies is obtained from one of the inequalities in the long-wavelength limit, and is generalized to arbitrary spatial dimensions.
Oscillator strength sum rules with an external electromagnetic field
NASA Astrophysics Data System (ADS)
Cabrera-Trujillo, R.; Sabin, John R.; Öhrn, Yngve; Oddershede, J.
1998-04-01
We demonstrate that the Bethe, and therefore the Thomas-Reiche-Kuhn, sum rule is unaffected by the presence of an applied external electromagnetic field in the exact case. We use the consequence that the first-order perturbation contribution must also vanish to derive a necessary condition for the completeness of computational one-electron basis sets.
Spectral sum rules for confining large-N theories
Cherman, Aleksey; McGady, David A.; Yamazaki, Masahito
2016-06-17
We consider asymptotically-free four-dimensional large-$N$ gauge theories with massive fermionic and bosonic adjoint matter fields, compactified on squashed three-spheres, and examine their regularized large-$N$ confined-phase spectral sums. The analysis is done in the limit of vanishing ’t Hooft coupling, which is justified by taking the size of the compactification manifold to be small compared to the inverse strong scale Λ₋1. We find our results motivate us to conjecture some universal spectral sum rules for these large $N$ gauge theories.
Spectral sum rules for confining large-N theories
Cherman, Aleksey; McGady, David A.; Yamazaki, Masahito
2016-06-17
We consider asymptotically-free four-dimensional large-$N$ gauge theories with massive fermionic and bosonic adjoint matter fields, compactified on squashed three-spheres, and examine their regularized large-$N$ confined-phase spectral sums. The analysis is done in the limit of vanishing ’t Hooft coupling, which is justified by taking the size of the compactification manifold to be small compared to the inverse strong scale Λ^{₋1}. We find our results motivate us to conjecture some universal spectral sum rules for these large $N$ gauge theories.
NASA Astrophysics Data System (ADS)
Kharitonov, Maxim; Andrei, Natan; Coleman, Piers
2013-03-01
We calculate the single-particle Green's functions and scattering amplitudes of the one-channel and channel-anisotropic two-channel Kondo models at the Toulouse and Emery-Kivelson lines, respectively, where exact solutions via the bosonization-refermionization approach are admitted. We demonstrate that in this approach the Friedel sum rules - the relations between the trapped spin and ``flavor'' moments and the scattering phase shifts in the Fermi-liquid regime - arise naturally and elucidate on their subtleties. We also recover the ``unitarity paradox'' - the vanishing of the single-particle scattering amplitude at the channel-symmetric point of the two-channel Kondo model - stemming from non-Fermi-liquid behavior. We discuss the implications of these results for the development of composite pairing in heavy fermion systems. This work was supported by National Science Foundation grants DMR 0907179 (MK, PC) and DMR 1006684 (NA).
Strange quark condensate from QCD sum rules to five loops
NASA Astrophysics Data System (ADS)
Dominguez, Cesareo A.; Nasrallah, Nasrallah F.; Schilcher, Karl
2008-02-01
It is argued that it is valid to use QCD sum rules to determine the scalar and pseudoscalar two-point functions at zero momentum, which in turn determine the ratio of the strange to non-strange quark condensates Rsu = langlebar ssrangle/langlebar qqrangle with (q = u, d). This is done in the framework of a new set of QCD Finite Energy Sum Rules (FESR) that involve as integration kernel a second degree polynomial, tuned to reduce considerably the systematic uncertainties in the hadronic spectral functions. As a result, the parameters limiting the precision of this determination are ΛQCD, and to a major extent the strange quark mass. From the positivity of Rsu there follows an upper bound on the latter: \\overline{ms}(2 GeV) <= 121 (105) MeV, for ΛQCD = 330 (420) MeV.
Circulation-strain sum rule in stochastic magnetohydrodynamics.
Moriconi, L; Nobre, F A S
2002-03-01
We study probability density functions (PDFs) of the circulation of velocity and magnetic fields in magnetohydrodynamics, computed for a circular contour within inertial range scales. The analysis is based on the instanton method as adapted to the Martin-Siggia-Rose field theory formalism. While in the viscous limit the expected Gaussian behavior of fluctuations is indeed verified, the case of vanishing viscosity is not suitable of a direct saddle-point treatment. To study the latter limit, we take into account fluctuations around quasistatic background fields, which allows us to derive a sum rule relating PDFs of the circulation observables and the rate of the strain tensor. A simple inspection of the sum rule definition leads straightforwardly to the algebraic decay rho(Gamma)-1/Gamma(2) at the circulation PDF tails.
Otto Stern, the Gdh Sum Rule and Various Spin Crises
NASA Astrophysics Data System (ADS)
Drechsel, D.
2001-02-01
The history of spin and anomalous magnetic moment is full of puzzles and "crises" from the first observations in the 1920's to the present day. The Gerasimov-Drell-Hearn sum rule connects the anomalous magnetic moment with the helicity dependent cross section for photoproduction, and as such checks the internal consistency of our understanding of the nucleon spin structure. Various generalizations of the sum rule have been proposed for the case of virtual photons, thus interpolating from the real photon point to deep inelastic scattering. A series of recent and newly proposed experiments with beam and target/recoil polarization will study this transition between the coherent spin-dependent response and the incoherent response of the partons in the scaling region.
Photonuclear sum rules and the tetrahedral configuration of He4
NASA Astrophysics Data System (ADS)
Gazit, Doron; Barnea, Nir; Bacca, Sonia; Leidemann, Winfried; Orlandini, Giuseppina
2006-12-01
Three well-known photonuclear sum rules (SR), i.e., the Thomas-Reiche-Kuhn, the bremsstrahlungs and the polarizability SR are calculated for He4 with the realistic nucleon-nucleon potential Argonne V18 and the three-nucleon force Urbana IX. The relation between these sum rules and the corresponding energy weighted integrals of the cross section is discussed. Two additional equivalences for the bremsstrahlungs SR are given, which connect it to the proton-neutron and neutron-neutron distances. Using them, together with our result for the bremsstrahlungs SR, we find a deviation from the tetrahedral symmetry of the spatial configuration of He4. The possibility to access this deviation experimentally is discussed.
Heavy-meson decay constants from QCD sum rules
Lucha, Wolfgang; Melikhov, Dmitri; Simula, Silvano
2010-12-22
We sketch a recent sum-rule extraction of the decay constants of the heavy pseudoscalar mesons D, D{sub s}, B, and B{sub s} from the two-point correlator of heavy-light pseudoscalar currents. Our main emphasis lies on the control over all the uncertainties in the decay constants, related both to the input QCD parameters and to the limited accuracy of the method of sum rules. Gaining this control has become possible by application of our new procedure of extracting hadron observables based on a dual threshold depending on the Borel parameter. For the charmed-meson decay constants, we find fD = (206.2{+-}7.3{sub (OPE)}{+-}5.1{sub (syst)}) MeV, fD{sub s} = (245.3{+-}15.7{sub (OPE)}{+-}4.5{sub (syst)}) MeV. For the beauty mesons, the decay constants turn out to be extremely sensitive to the precise value of the {ovr MS} mass of the b-quark, {bar m}{sub b}({bar m}{sub b}). By requiring our sum-rule estimate to match the average of the lattice determinations of f{sub B}, we extract the rather accurate value {bar m}{sub b}({bar m}{sub b}) = (4.245{+-}0.025) GeV. Feeding this parameter value into our sum-rule formalism leads to the beauty-meson decay constants fB = (193.4{+-}12.3{sub (OPE)}{+-}4.3{sub (syst)}) MeV, fB{sub s} = (232.5{+-}18.6{sub (OPE)}{+-}2.4{sub (syst)}) MeV.
A QCD Sum Rules Approach to Mixing of Hadrons
Aliev, T. M.; Ozpineci, A.; Zamiralov, V. S.
2010-12-28
A method for the calculation of the hadronic mixing angles using QCD sum rules is proposed. This method is then applied to predict the mixing angle between the heavy cascade hyperons {Xi}{sub Q} and {Xi}{sub Q}{sup '} where Q = c or Q = b. It is obtained the {theta}{sub b} = 6.4 deg. {+-}1.8 deg. and {theta}{sub c} = 5.5 deg. {+-}1.8 deg.
On the loop approximation in nucleon QCD sum rules
Drukarev, E. G. Ryskin, M. G.; Sadovnikova, V. A.
2015-10-15
There was a general belief that the nucleon QCD sum rules which include only the quark loops and thus contain only the condensates of dimension d = 3 and d = 4 have only a trivial solution. We demonstrate that there is also a nontrivial solution. We show that it can be treated as the lowest order approximation to the solution which includes the higher terms of the Operator Product Expansion. Inclusion of the radiative corrections improves the convergence of the series.
Renormalisation group corrections to neutrino mixing sum rules
NASA Astrophysics Data System (ADS)
Gehrlein, J.; Petcov, S. T.; Spinrath, M.; Titov, A. V.
2016-11-01
Neutrino mixing sum rules are common to a large class of models based on the (discrete) symmetry approach to lepton flavour. In this approach the neutrino mixing matrix U is assumed to have an underlying approximate symmetry form Ũν, which is dictated by, or associated with, the employed (discrete) symmetry. In such a setup the cosine of the Dirac CP-violating phase δ can be related to the three neutrino mixing angles in terms of a sum rule which depends on the symmetry form of Ũν. We consider five extensively discussed possible symmetry forms of Ũν: i) bimaximal (BM) and ii) tri-bimaximal (TBM) forms, the forms corresponding to iii) golden ratio type A (GRA) mixing, iv) golden ratio type B (GRB) mixing, and v) hexagonal (HG) mixing. For each of these forms we investigate the renormalisation group corrections to the sum rule predictions for δ in the cases of neutrino Majorana mass term generated by the Weinberg (dimension 5) operator added to i) the Standard Model, and ii) the minimal SUSY extension of the Standard Model.
Relativistic and Nuclear Medium Effects on the Coulomb Sum Rule
NASA Astrophysics Data System (ADS)
Cloët, Ian C.; Bentz, Wolfgang; Thomas, Anthony W.
2016-01-01
In light of the forthcoming high precision quasielastic electron scattering data from Jefferson Lab, it is timely for the various approaches to nuclear structure to make robust predictions for the associated response functions. With this in mind, we focus here on the longitudinal response function and the corresponding Coulomb sum rule for isospin-symmetric nuclear matter at various baryon densities. Using a quantum field-theoretic quark-level approach which preserves the symmetries of quantum chromodynamics, as well as exhibiting dynamical chiral symmetry breaking and quark confinement, we find a dramatic quenching of the Coulomb sum rule for momentum transfers |q |≳0.5 GeV . The main driver of this effect lies in changes to the proton Dirac form factor induced by the nuclear medium. Such a dramatic quenching of the Coulomb sum rule was not seen in a recent quantum Monte Carlo calculation for carbon, suggesting that the Jefferson Lab data may well shed new light on the explicit role of QCD in nuclei.
Relativistic and Nuclear Medium Effects on the Coulomb Sum Rule.
Cloët, Ian C; Bentz, Wolfgang; Thomas, Anthony W
2016-01-22
In light of the forthcoming high precision quasielastic electron scattering data from Jefferson Lab, it is timely for the various approaches to nuclear structure to make robust predictions for the associated response functions. With this in mind, we focus here on the longitudinal response function and the corresponding Coulomb sum rule for isospin-symmetric nuclear matter at various baryon densities. Using a quantum field-theoretic quark-level approach which preserves the symmetries of quantum chromodynamics, as well as exhibiting dynamical chiral symmetry breaking and quark confinement, we find a dramatic quenching of the Coulomb sum rule for momentum transfers |q|≳0.5 GeV. The main driver of this effect lies in changes to the proton Dirac form factor induced by the nuclear medium. Such a dramatic quenching of the Coulomb sum rule was not seen in a recent quantum Monte Carlo calculation for carbon, suggesting that the Jefferson Lab data may well shed new light on the explicit role of QCD in nuclei.
Electric-dipole sum rule in nuclear matter
NASA Astrophysics Data System (ADS)
Fabrocini, A.; Fantoni, S.
1985-03-01
The enhancement factor K in the electric-dipole sum rule for some realistic models of symmetrical nuclear matter is calculated using variational theory. The nuclear-matter wave function used contains central, spin, isospin, tensor and spin-orbit pair correlations. The non-central correlations, particularly the tensor one, give the major contribution to K. At experimental equilibrium density K. turns out to be ≈ 1.8, of which 65% comes from OPEP and 30% from the short-range part of the interaction. The two-pion-exchange three-nucleon interaction contributes ≈ 0.2% and is cancelled, to a large extent, by the contribution due to the intermediate-range two-body potential. The relationship of the summed oscillator strength with the effective mass is also discussed.
Peiponen, Kai-Erik; Saarinen, Jarkko J.; Svirko, Yuri
2004-04-01
Dispersion relations and sum rules for nonlinear susceptibilities are derived using complex analysis and especially the concept of a meromorphic function. The dispersion relations and sum rules provide frames to investigate the consistency between the theory and experiments.
Sum rules and photon emission in hadronic matter
NASA Astrophysics Data System (ADS)
Holt, Nathan Prescott Montgomery
In this work, we examine properties of quantum chromodynamics (QCD) at moderate temperatures and density. These conditions are reached in the later stages of ultra-relativistic heavy-ion collisions after the matter has cooled sufficiently to re-hadronize from a quark-gluon plasma. The properties of matter in this stage are expected to change smoothly with temperature. We explore this behavior in two ways. First, we use finite-temperature sum rules to analyze the properties of vector and axial-vector spectral functions at low temperatures. Previous models used in sum rule analyses frequently led to ambiguous applications. Here we avoid such ambiguities by using an improved vacuum spectral function model together with a strict leading-order-in-temperature expansion. This results in well-defined finite temperature spectral functions. Additionally, we incorporate a finite pion mass, which we show induces an analytical violation of the sum rules. We then proceed to numerically measure that violation. Second, we calculate thermal photon emissivities of QCD matter from interactions involving both mesons and baryons. We identify a novel source of thermal photons from a system composed of pi, rho, and o mesons, then calculate photon emission rates from this system using both relativistic kinetic theory and thermal field theory. These rates are compared to existing calculations and found to be significant. We then calculate thermal photon emission rates from baryon interactions, using an exhaustive set of both strange and non-strange particles. We again find novel sources of photons from this system, compare the total rates to calculations of current state-of-the-art photon emission rates, and find them to be comparable.
Sum rule study for double Gamow-Teller states
NASA Astrophysics Data System (ADS)
Sagawa, H.; Uesaka, T.
2016-12-01
We study the sum rules of double Gamow-Teller (DGT) excitations through double spin-isospin operator (σt-) 2. In general, 2+ states in the grand-daughter nuclei have dominant transition strength in DGT excitations and 0+ states are weak, except in T =1 mother nuclei in which 0+ strength is competitive with 2+ strength. The isospin selection of DGT is also discussed among five possible isospin states in grand-daughter nuclei. A possibility to extract the unit cross section for the DGT transition strength is pointed out in the (σt-) 2 excitation of double isobaric analog state (DIAS) in T =1 nuclei.
Justifying the naive partonic sum rule for proton spin
Ji, Xiangdong; Zhang, Jian-Hui; Zhao, Yong
2015-04-01
We provide a theoretical basis for understanding the spin structure of the proton in terms of the spin and orbital angular momenta of free quarks and gluons in Feynman’s parton picture. We show that each term in the Jaffe–Manohar spin sum rule can be related to the matrix element of a gauge-invariant, but frame-dependent operator through a matching formula in large-momentum effective field theory. We present all the matching conditions for the spin content at one-loop order in perturbation theory, which provide a basis to calculate parton orbital angular momentum in lattice QCD at leading logarithmic accuracy.
3He Spin-Dependent Cross Sections and Sum Rules
Slifer, Karl; Amaryan, Moscov; Amaryan, Moskov; Auerbach, Leonard; Averett, Todd; Berthot, J.; Bertin, Pierre; Bertozzi, William; Black, Tim; Brash, Edward; Brown, D.; Burtin, Etienne; Calarco, John; Cates, Gordon; Chai, Zhengwei; Chen, Jian-Ping; Choi, Seonho; Chudakov, Eugene; Ciofi, Claudio; Cisbani, Evaristo; De Jager, Cornelis; Deur, Alexandre; DiSalvo, R.; Dieterich, Sonja; Djawotho, Pibero; Finn, John; Fissum, Kevin; Fonvieille, Helene; Frullani, Salvatore; Gao, Haiyan; Gao, Juncai; Garibaldi, Franco; Gasparian, Ashot; Gilad, Shalev; Gilman, Ronald; Glamazdin, Oleksandr; Glashausser, Charles; Glockle, W.; Golak, J.; Goldberg, Emma; Gomez, Javier; Gorbenko, Viktor; Hansen, Jens-Ole; Hersman, F.; Holmes, Richard; Huber, Garth; Hughes, Emlyn; Humensky, Thomas; Incerti, Sebastien; Iodice, Mauro; Jensen, S.; Jiang, Xiaodong; Jones, C.; Jones, G.; Jones, Mark; Jutier, Christophe; Kamada, H.; Ketikyan, Armen; Kominis, Ioannis; Korsch, Wolfgang; Kramer, Kevin; Kumar, Krishna; Kumbartzki, Gerfried; Kuss, Michael; Lakuriqi, Enkeleida; Laveissiere, Geraud; LeRose, John; Liang, Meihua; Liyanage, Nilanga; Lolos, George; Malov, Sergey; Marroncle, Jacques; McCormick, Kathy; McKeown, Robert; Meziani, Zein-Eddine; Michaels, Robert; Mitchell, Joseph; Nogga, Andreas; Pace, Emanuele; Papandreou, Zisis; Pavlin, Tina; Petratos, Gerassimos; Pripstein, David; Prout, David; Ransome, Ronald; Roblin, Yves; Rowntree, David; Rvachev, Marat; Sabatie, Franck; Saha, Arunava; Salme, Giovanni; SCOPETTA, S.; Skibinski, R.; Souder, Paul; Saito, Teijiro; Strauch, Steffen; Suleiman, Riad; Takahashi, Kazunori; Todor, Luminita; Tsubota, Hiroaki; Ueno, Hiroaki; Urciuoli, Guido; van der Meer, Rob; Vernin, Pascal; Voskanyan, Hakob; Witala, Henryk; Wojtsekhowski, Bogdan; Xiong, Feng; Xu, Wang; Yang, Jae-Choon; Zhang, Bin; Zolnierczuk, Piotr
2008-07-01
We present a measurement of the spin-dependent cross sections for the \\vec{^3He}(\\vec{e},e')X} reaction in the quasielastic and resonance regions at four-momentum transfer 0.1 < Q^2< 0.9 GeV^2. The spin-structure functions have been extracted and used to evaluate the nuclear Burkhardt--Cottingham and extended GDH sum rules for the first time. Impulse approximation and exact three-body Faddeev calculations are also compared to the data in the quasielastic region.
Light-Cone Sum Rule Approach for Baryon Form Factors
NASA Astrophysics Data System (ADS)
Offen, Nils
2016-10-01
We present the state-of-the-art of the light-cone sum rule approach to Baryon form factors. The essence of this approach is that soft Feynman contributions are calculated in terms of small transverse distance quantities using dispersion relations and duality. The form factors are thus expressed in terms of nucleon wave functions at small transverse separations, called distribution amplitudes, without any additional parameters. The distribution amplitudes, therefore, can be extracted from the comparison with the experimental data on form factors and compared to the results of lattice QCD simulations.
3He spin-dependent cross sections and sum rules.
Slifer, K; Amarian, M; Auerbach, L; Averett, T; Berthot, J; Bertin, P; Bertozzi, B; Black, T; Brash, E; Brown, D; Burtin, E; Calarco, J; Cates, G; Chai, Z; Chen, J-P; Choi, Seonho; Chudakov, E; Ciofi Degli Atti, C; Cisbani, E; de Jager, C W; Deur, A; DiSalvo, R; Dieterich, S; Djawotho, P; Finn, M; Fissum, K; Fonvieille, H; Frullani, S; Gao, H; Gao, J; Garibaldi, F; Gasparian, A; Gilad, S; Gilman, R; Glamazdin, A; Glashausser, C; Glöckle, W; Golak, J; Goldberg, E; Gomez, J; Gorbenko, V; Hansen, J-O; Hersman, B; Holmes, R; Huber, G M; Hughes, E; Humensky, B; Incerti, S; Iodice, M; Jensen, S; Jiang, X; Jones, C; Jones, G; Jones, M; Jutier, C; Kamada, H; Ketikyan, A; Kominis, I; Korsch, W; Kramer, K; Kumar, K; Kumbartzki, G; Kuss, M; Lakuriqi, E; Laveissiere, G; Lerose, J J; Liang, M; Liyanage, N; Lolos, G; Malov, S; Marroncle, J; McCormick, K; McKeown, R D; Meziani, Z-E; Michaels, R; Mitchell, J; Nogga, A; Pace, E; Papandreou, Z; Pavlin, T; Petratos, G G; Pripstein, D; Prout, D; Ransome, R; Roblin, Y; Rowntree, D; Rvachev, M; Sabatié, F; Saha, A; Salmè, G; Scopetta, S; Skibiński, R; Souder, P; Saito, T; Strauch, S; Suleiman, R; Takahashi, K; Teijiro, S; Todor, L; Tsubota, H; Ueno, H; Urciuoli, G; Van der Meer, R; Vernin, P; Voskanian, H; Witała, H; Wojtsekhowski, B; Xiong, F; Xu, W; Yang, J-C; Zhang, B; Zolnierczuk, P
2008-07-11
We present a measurement of the spin-dependent cross sections for the 3He over -->(e over -->,e')X reaction in the quasielastic and resonance regions at a four-momentum transfer 0.1< or =Q2< or =0.9 GeV2. The spin-structure functions have been extracted and used to evaluate the nuclear Burkhardt-Cottingham and extended Gerasimov-Drell-Hearn sum rules for the first time. The data are also compared to an impulse approximation calculation and an exact three-body Faddeev calculation in the quasielastic region.
Sum-rule constraints on possible diphoton resonances at LHC
NASA Astrophysics Data System (ADS)
Roig, P.; Sanz-Cillero, J. J.
2017-03-01
The study of the forward scattering amplitude V(k, λ)V(k'λ') → V(k, λ)V(k', λ') of real massless gauge bosons V, e.g. photons or gluons, leads to a sumrule that can be used to investigate beyond the Standard Model signals at LHC in the γγ channel. The sum-rule only relies on general properties such as analyticity, unitarity and crossing. We use the now buried "750 GeV diphoton resonance" as a case of study to exemplify the constraints that the forward sum-rule requires to any new physics candidate. In the case of a large γγ or gg partial width, of the order of 10 GeV in our 750 GeV analysis, one finds that an infinite tower of states with spin JR = 2 and higher must be ultimately incorporated to the beyond Standard Model theory in order to fulfill the sumrule. We expect these techniques may be useful in next diphoton searches at LHC and future colliders.
Sum Rules and Moments of the Nucleon Spin Structure Functions
Jian-Ping Chen; Alexandre Deur; Zein-Eddine Meziani
2005-08-01
The nucleon has been used as a laboratory to investigate its own spin structure and Quantum Chromodynamics. New experimental data on nucleon spin structure at low to intermediate momentum transfers combined with existing high momentum transfer data offer a comprehensive picture of the transition region from the confinement regime of the theory to its asymptotic freedom regime. Insight for some aspects of the theory is gained by exploring lower moments of spin structure functions and their corresponding sum rules (i.e. the Gerasimov-Drell-Hearn, Bjorken and Burkhardt-Cottingham). These moments are expressed in terms of an operator product expansion using quark and gluon degrees of freedom at moderately large momentum transfers. The sum rules are verified to a good accuracy assuming that no singular behavior of the structure functions is present at very high excitation energies. The higher twist contributions have been examined through the moments evolution as the momentum transfer varies from higher to lower values. Furthermore, QCD-inspired low energy effective theories, which explicitly include chiral symmetry breaking, are tested at low momentum transfers. The validity of these theories is further examined as the momentum transfer increases to moderate values. It is found that chiral perturbation calculations agree reasonably well with the first moment of the spin structure function g{sub 1} at momentum transfer of 0.1 GeV{sup 2} but fail to reproduce the neutron data in the case of the generalized polarizability {delta}{sub LT}.
On properties of the exotic hadrons from QCD sum rules
NASA Astrophysics Data System (ADS)
Lucha, Wolfgang; Melikhov, Dmitri
2016-11-01
We discuss the specific features of extracting properties of the exotic polyquark hadrons (tetraquarks, pentaquarks) compared to the usual hadrons by the QCD sum-rule approach. In the case of the ordinary hadrons, already the one-loop leading-order O(α0s) correlation functions provide the bulk of the hadron observables, e.g., of the form factor; inclusion of radiative corrections O(αs) modifies already nonzero one-loop contributions. In the case of an exotic hadron, the situation is qualitatively different: discussing strong decays of an exotic tetraquark meson, which provide the main contribution to its width, we show that the disconnected leading-order diagrams are not related to the tetraquark properties. For a proper description of the tetraquark decay width, it is mandatory to calculate specific radiative corrections which generate the connected diagrams.
Spectral sum rules and search for periodicities in DNA sequences
NASA Astrophysics Data System (ADS)
Chechetkin, V. R.
2011-04-01
Periodic patterns play the important regulatory and structural roles in genomic DNA sequences. Commonly, the underlying periodicities should be understood in a broad statistical sense, since the corresponding periodic patterns have been strongly distorted by the random point mutations and insertions/deletions during molecular evolution. The latent periodicities in DNA sequences can be efficiently displayed by Fourier transform. The criteria of significance for observed periodicities are obtained via the comparison versus the counterpart characteristics of the reference random sequences. We show that the restrictions imposed on the significance criteria by the rigorous spectral sum rules can be rationally described with De Finetti distribution. This distribution provides the convenient intermediate asymptotic form between Rayleigh distribution and exact combinatoric theory.
Moments of Spin Structure Functions: Sum Rules and Polarizabilities
Jian-Ping Chen
2010-10-01
Nucleon structure study is one of the most important research areas in modern physics and has challenged us for decades. Spin has played an essential role and often brought surprises and puzzles to the investigation of the nucleon structure and the strong interaction. New experimental data on nucleon spin structure at low to intermediate momentum transfers combined with existing high momentum transfer data offer a comprehensive picture in the strong region of the interaction and of the transition region from the strong to the asymptotic-free region. Insight for some aspects of the theory for the strong interaction, Quantum Chromodynamics (QCD), is gained by exploring lower moments of spin structure functions and their corresponding sum rules (i.e. the Bjorken, Burkhardt-Cottingham, Gerasimov-Drell-Hearn (GDH), and the generalized GDH). These moments are expressed in terms of an operator-product expansion using quark and gluon degrees of freedom at moderately large momentum transfers.
The DHG sum rule measured with medium energy photons
Hicks, K.; Ardashev, K.; Babusci, D.
1997-12-31
The structure of the nucleon has many important features that are yet to be uncovered. Of current interest is the nucleon spin-structure which can be measured by doing double-polarization experiments with photon beams of medium energies (0.1 to 2 GeV). One such experiment uses dispersion relations, applied to the Compton scattering amplitude, to relate measurement of the total reaction cross section integrated over the incident photon energy to the nucleon anomalous magnetic moment. At present, no single facility spans the entire range of photon energies necessary to test this sum rule. The Laser-Electron Gamma Source (LEGS) facility will measure the double-polarization observables at photon energies between 0.15--0.47 MeV. Either the SPring8 facility, the GRAAL facility (France), or Jefferson Laboratory could make similar measurements at higher photon energies. A high-precision measurement of the spin-polarizability and the Drell-Hearn-Gerasimov sum rule is now possible with the advent of high-polarization solid HD targets at medium energy polarized photon facilities such as LEGS, GRAAL and SPring8. Other facilities with lower polarization in either the photon beam or target (or both) are also pursuing these measurements because of the high priority associated with this physics. The Spin-asymmetry (SASY) detector that will be used at LEGS has been briefly outlined in this paper. The detector efficiencies have been explored with simulations studies using the GEANT software, with the result that both charged and uncharged pions can be detected with a reasonable efficiency (> 30%) over a large solid angle. Tracking with a TPC, which will be built at LEGS over the next few years, will improve the capabilities of these measurements.
Impact of Duality Violations on Spectral Sum Rule analyses
NASA Astrophysics Data System (ADS)
Catà, Oscar
2007-02-01
Recent sum rule analyses on the
Comparing T-odd and T-even spin sum rules
Teryaev, O.V.
2015-04-10
Sum rules for T-even and T-odd structure functions and parton distributions are considered. The case of spin-dependent distributions related to energy-momentum tensor (EMT) is specifically addressed. The Burkardt sum rule for T-odd Sivers functions may be related to EMT provided the imaginary prescription for gluonic pole correlator is incorporated. The momentum sum rule for deuteron tensor spin structure function allows one to probe indirectly the gravity couplings to quarks and gluons.
Symbolic methods for the evaluation of sum rules of Bessel functions
Babusci, D.; Dattoli, G.; Górska, K.; Penson, K. A.
2013-07-15
The use of the umbral formalism allows a significant simplification of the derivation of sum rules involving products of special functions and polynomials. We rederive in this way known sum rules and addition theorems for Bessel functions. Furthermore, we obtain a set of new closed form sum rules involving various special polynomials and Bessel functions. The examples we consider are relevant for applications ranging from plasma physics to quantum optics.
Comparing T-odd and T-even spin sum rules
NASA Astrophysics Data System (ADS)
Teryaev, O. V.
2015-04-01
Sum rules for T-even and T-odd structure functions and parton distributions are considered. The case of spin-dependent distributions related to energy-momentum tensor (EMT) is specifically addressed. The Burkardt sum rule for T-odd Sivers functions may be related to EMT provided the imaginary prescription for gluonic pole correlator is incorporated. The momentum sum rule for deuteron tensor spin structure function allows one to probe indirectly the gravity couplings to quarks and gluons.
QCD sum rule study of hidden-charm pentaquarks
NASA Astrophysics Data System (ADS)
Chen, Hua-Xing; Cui, Er-Liang; Chen, Wei; Liu, Xiang; Steele, T. G.; Zhu, Shi-Lin
2016-10-01
We study the mass spectra of hidden-charm pentaquarks having spin J = {1over 2}/{3over 2}/{5over 2} and quark contents uud c bar{c}. We systematically construct all the relevant local hidden-charm pentaquark currents, and we select some of them to perform QCD sum rule analyses. We find that the P_c(4380) and P_c(4450) can be identified as hidden-charm pentaquark states composed of an anti-charmed meson and a charmed baryon. Besides them, we also find (a) the lowest-lying hidden-charm pentaquark state of J^P = 1/2^- has the mass 4.33^{+0.17}_{-0.13} GeV, while the one of J^P = 1/2^+ is significantly higher, that is, around 4.7-4.9 GeV; (b) the lowest-lying hidden-charm pentaquark state of J^P = 3/2^- has the mass 4.37^{+0.18}_{-0.13} GeV, consistent with the P_c(4380) of J^P = 3/2^-, while the one of J^P = 3/2^+ is also significantly higher, that is, above 4.6 GeV; (c) the hidden-charm pentaquark state of J^P = 5/2^- has a mass around 4.5-4.6 GeV, slightly larger than the P_c(4450) of J^P = 5/2^+.
D -wave charmed and bottomed baryons from QCD sum rules
NASA Astrophysics Data System (ADS)
Chen, Hua-Xing; Mao, Qiang; Hosaka, Atsushi; Liu, Xiang; Zhu, Shi-Lin
2016-12-01
We study the D -wave charmed baryons of S U (3 ) flavor 3¯ F using the method of QCD sum rules in the framework of heavy quark effective theory. We find that the Λc(2880 ), Ξc(3055 ), and Ξc(3080 ) can be well described by the D -wave S U (3 ) 3¯F charmed baryon multiplets of JP=3 /2+ and 5 /2+, which contain two λ -mode orbital excitations; i.e., the Λc(2880 ) has JP=5 /2+, and the Ξc(3055 ) and Ξc(3080 ) have JP=3 /2+ and 5 /2+, respectively. Our results also suggest that the Λc(2880 ) has a partner state, the Λc(3 /2+) of JP=3 /2+. Its mass is around 2.8 1-0.18+0.33 GeV , and the mass difference between it and the Λc(2880 ) is 2 8-24+45 MeV . We also evaluate the masses of their bottom partners.
Sum rules for nuclear excitations with the Skyrme-Landau interaction
NASA Astrophysics Data System (ADS)
Liu, Keh-Fei; Luo, Hong-De; Ma, Zhongyu; Feng, Man; Shen, Qing-Biao
1991-11-01
The energy-weighted sum rules for electric, magnetic, Fermi and Gamow-Teller transitions with the Skyrme-Landau interaction are derived from the double commutators and numerically calculated in a HF+RPA formalism. As a numerical check of the Thouless theorem, our self-consistent calculations show that the calculated RPA strengths exhaust more than 85% of the sum rules in most cases. The well known non-energy-weighted sum rules for Fermi and Gamow-Teller transitions are also checked numerically. The sum rules are exhausted by more than 94% in these cases.
NASA Astrophysics Data System (ADS)
Karlsson, Daniel; van Leeuwen, Robert
2016-09-01
We consider a general class of approximations which guarantees the conservation of particle number in many-body perturbation theory. To do this we extend the concept of Φ derivability for the self-energy Σ to a larger class of diagrammatic terms in which only some of the Green's function lines contain the fully dressed Green's function G . We call the corresponding approximations for Σ partially Φ derivable. A special subclass of such approximations, which are gauge invariant, is obtained by dressing loops in the diagrammatic expansion of Φ consistently with G . These approximations are number conserving but do not have to fulfill other conservation laws, such as the conservation of energy and momentum. From our formalism we can easily deduce whether commonly used approximations will fulfill the continuity equation, which implies particle number conservation. We further show how the concept of partial Φ derivability plays an important role in the derivation of a generalized sum rule for the particle number, which reduces to the Luttinger-Ward theorem in the case of a homogeneous electron gas, and the Friedel sum rule in the case of the Anderson model. To do this we need to ensure that the Green's function has certain complex analytic properties, which can be guaranteed if the spectral function is positive-semidefinite. The latter property can be ensured for a subset of partially Φ -derivable approximations for the self-energy, namely those that can be constructed from squares of so-called half diagrams. For the case in which the analytic requirements are not fulfilled we highlight a number of subtle issues related to branch cuts, pole structure, and multivaluedness. We also show that various schemes of computing the particle number are consistent for particle number conserving approximations.
Comparison of nuclear Hamiltonians using spectral function sum rules
NASA Astrophysics Data System (ADS)
Rios, A.; Carbone, A.; Polls, A.
2017-07-01
Background: The energy weighted sum rules of the single-particle spectral functions provide a quantitative understanding of the fragmentation of nuclear states due to short-range and tensor correlations. Purpose: The aim of this paper is to compare on a quantitative basis the single-particle spectral function generated by different nuclear Hamiltonians in symmetric nuclear matter using the first three energy-weighted moments. Method: The spectral functions are calculated in the framework of the self-consistent Green's function approach at finite temperature within a ladder resummation scheme. We analyze the first three moments of the spectral function and connect these to the correlations induced by the interactions between the nucleons in symmetric nuclear matter. In particular, the variance of the spectral function is directly linked to the dispersive contribution of the self-energy. The discussion is centered around two- and three-body chiral nuclear interactions, with and without renormalization, but we also provide results obtained with the traditional phase-shift-equivalent CD-Bonn and Av18 potentials. Results: The variance of the spectral function is particularly sensitive to the short-range structure of the force, with hard-core interactions providing large variances. Chiral forces yield variances which are an order of magnitude smaller and, when tamed using the similarity renormalization group, the variance reduces significantly and in proportion to the renormalization scale. The presence of three-body forces does not substantially affect the results. Conclusions: The first three moments of the spectral function are useful tools in analyzing the importance of correlations in nuclear ground states. In particular, the second-order moment provides a direct insight into dispersive contributions to the self-energy and its value is indicative of the fragmentation of single-particle states.
Photo-absorption sum rules σ-1 in different environments (Atoms, nuclei, nucleons)
NASA Astrophysics Data System (ADS)
Gerasimov, S. B.
2017-01-01
Combining the spin-dependent dispersion GDH-sum rule, the isotopic-spin-dependent Cabibbo-Radicati sum rule, and the relativistic dipole-moment-fluctuation (i.e. generalized Gottfried) sum rule with the three valence quark configuration of nucleons taken into account for the composition of the ground and the excited states of the nucleon, the relevant moments of the distribution and correlation functions of the quark electric dipole moment operators in the nucleon ground state are expressed via the experimentally measurable nucleon resonance photo-excitation amplitudes.These functions are of interest for checking detailed quark-configuration structure of the nucleon state vector. Within the non-relativistic approach to photo-absorption sum rules for the 3N-nuclei a new σ-1 sum rule proposed which is based on general charge-symmetry (CS) consequences for the "CS-conjugated" triton and 3He.
NASA Astrophysics Data System (ADS)
Gubler, Philipp; Satow, Daisuke
2016-11-01
We derive three exact sum rules for the spectral function of the electromagnetic current with zero spatial momentum at finite temperature. Two of them are derived in this paper for the first time. We explicitly check that these sum rules are satisfied in the weak coupling regime and examine which sum rule is sensitive to the transport peak in the spectral function at low energy or the continuum at high energy. Possible applications of the three sum rules to lattice computations of the spectral function and transport coefficients are also discussed: we propose an Ansatz for the spectral function that can be applied to all three sum rules and fit it to available lattice data of the Euclidean vector correlator above the critical temperature. As a result, we obtain estimates for both the electrical conductivity σ and the second-order transport coefficient τJ .
NASA Astrophysics Data System (ADS)
Satow, Daisuke; Gubler, Philipp
2017-03-01
We derive three exact sum rules for the spectral function of the electromagnetic current with zero spatial momentum at finite temperature. Possible applications of the three sum rules to lattice computations of the spectral function and transport coefficients are also discussed: We propose an ansatz for the spectral function that can be applied to all three sum rules and fit it to available lattice data of the Euclidean vector correlator above the critical temperature. As a result, we obtain estimates for both the electrical conductivity σ and the second order transport coefficient τJ.
Rate and CP-Asymmetry Sum Rules in B to K pi
Gronau, Michael; Rosner, Jonathan L.
2006-08-28
The observed violation of A{sub CP}(B{sup 0} {yields} K{sup +}{pi}{sup -}) = A{sub CP}(B{sup +} {yields} K{sup +}{pi}{sup 0}) has been recently mentioned as a puzzle for the standard model. They point out that while this violation may be accounted for by a large color-suppressed tree amplitude, a sum rule involving three or four B {yields} K{pi} CP asymmetries should hold. the current experimental status of these sum rules and of a sum rule for B {yields} K{pi} decay rates is presented.
Light-by-light forward scattering sum rules for charmonium states
NASA Astrophysics Data System (ADS)
Danilkin, Igor; Vanderhaeghen, Marc
2017-09-01
We apply three forward light-by-light scattering sum rules to charmonium states. We show that these sum rules imply a cancellation between charmonium bound state contributions, which are mostly known from the γ γ decay widths of these states, and continuum contributions above D D ¯ threshold, for which we provide a duality estimate. We also show that two of these sum rules allow us to predict the yet unmeasured γ*γ coupling of the χc 1(1 P ) state, which can be tested at present high-luminosity e+e- colliders.
The Gamow-Teller states and sum rule in relativistic models
NASA Astrophysics Data System (ADS)
Kurasawa, Haruki; Suzuki, Toshio; Van Giai, Nguyen
2004-02-01
The giant Gamow-Teller(GT) states and the CT sum rule are investigated in relativistic models. It is shown that the Ikeda-Fujii-Fujita sum rule value is quenched by 6% owing to relativistic effects. The quenched amount is taken by the nucleon-antinucleon states. This fact, together with the recent experiment which has observed 90% of the sum rule value, implies that the contribution of the Δ-hole states to the quenching is strongly reduced. As a result, the Landau-Migdal parameter g' NΔ which dominates the critical density of the pion condensation becomes much smaller than what was believed before.
Charmonia decay constants from the QCD lattice and QCD sum rules
NASA Astrophysics Data System (ADS)
Bečirević, Damir; Duplančić, Goran; Klajn, Bruno; Melić, Blaženka; Sanfillipo, Francesco
2016-04-01
Using lattice QCD and QCD sum rules we compute the lowest state charmonia JPC =0-+ (ηc), 1- (J / ψ), and 1+- (hc) decay constants. For calculating the decay constant of J / ψ we use both the vector and tensor currents and compare the results. Lattice QCD results are obtained from the unquenched (Nf = 2) simulations using twisted mass QCD at four lattice spacings and taking the continuum limit. In the QCD sum rule calculation we apply the moment sum rules. We also comment the phenomenological implications of calculated charmonia decay constants in ηc → γγ decay, and B →Xcc‾ K decays.
Truncated Sum Rules and Their Use in Calculating Fundamental Limits of Nonlinear Susceptibilities
NASA Astrophysics Data System (ADS)
Kuzyk, Mark G.
Truncated sum rules have been used to calculate the fundamental limits of the nonlinear susceptibilities and the results have been consistent with all measured molecules. However, given that finite-state models appear to result in inconsistencies in the sum rules, it may seem unclear why the method works. In this paper, the assumptions inherent in the truncation process are discussed and arguments based on physical grounds are presented in support of using truncated sum rules in calculating fundamental limits. The clipped harmonic oscillator is used as an illustration of how the validity of truncation can be tested and several limiting cases are discussed as examples of the nuances inherent in the method.
Models for relativistic coulomb sum rules: Expansions in moments of the nuclear momentum density
NASA Astrophysics Data System (ADS)
Donnelly, T. W.; Kronenberg, E. L.; Van Orden, J. W.
1989-04-01
Relativistic Coulomb sum rules for quasielastic electron scattering from nuclei are developed using a class of relativistic models for the nuclear ground-state momentum distribution. Approximate sum rules at constant 3- or 4-momentum transfer are expressed as expansions in moments of the momentum distribution. New sum-rule functions are derived which, even for very large values of energy and momentum where relativistic effects become dominant, approach simple asymptotic values; in doing so they approximately retain the flavor of the nonrelativistic Coulomb sum rule which approaches Z. Specific ways of achieving an optimum separation of effects relating to the electromagnetic response of a single nucleon and of a many-body system of structureless particles are discussed, including a study of sensitivities to alternative parameterizations of GEn. Comparisons of results using different momentum distributions for the case of 16O are presented.
Pascalutsa-Vanderhaeghen light-by-light sum rule from photon-photon collisions
NASA Astrophysics Data System (ADS)
Dai, Ling-Yun; Pennington, M. R.
2017-03-01
Light-by-light scattering sum rules based on general field theory principles relate cross sections with different helicities. In this paper the simplest sum rule is tested for the I =0 and 2 channels for "real" photon-photon collisions. Important contributions come from the long-lived pseudoscalar mesons and from dimeson intermediate states. The latest amplitude analysis of γ γ →π π ,K ¯K allows this contribution to be evaluated. However, we find that other multimeson contributions up to 2.5 GeV are required to satisfy the sum rules. While data on three- and four-pion cross sections exist, there is no information about their isospin and helicity decomposition. Nevertheless, we show the measured cross sections are sufficiently large to ensure the sum rules for the helicity differences are likely fulfilled.
Forward Compton scattering with weak neutral current: Constraints from sum rules
Gorchtein, Mikhail; Zhang, Xilin
2015-06-09
We generalize forward real Compton amplitude to the case of the interference of the electromagnetic and weak neutral current, formulate a low-energy theorem, relate the new amplitudes to the interference structure functions and obtain a new set of sum rules. Furthermore, we address a possible new sum rule that relates the product of the axial charge and magnetic moment of the nucleon to the 0th moment of the structure function g5(ν, 0). For the dispersive γ Z-box correction to the proton’s weak charge, the application of the GDH sum rule allows us to reduce the uncertainty due to resonance contributionsmore » by a factor of two. Finally, the finite energy sum rule helps addressing the uncertainty in that calculation due to possible duality violations.« less
Sum rules and static local-field corrections of electron liquids in two and three dimensions
NASA Technical Reports Server (NTRS)
Iwamoto, N.
1984-01-01
The dielectric functions of electron liquids which take into account short-range electron-electron correlations via the static local-field corrections are examined in the light of the frequency-moment sum rules. The formation is given for degenerate as well as classical electron liquids in arbitrary (d) spatial dimensions, which is suitable for comparison between the two- and three-dimensional cases. By using the virial equations of state it is shown that such dielectric functions cannot satisfy the compressibility sum rule and the third-frequency-moment sum rule simultaneously. In the degenerate case, the plasmon, single-pair, and multipair contributions to the sum rules are analyzed, and the reason for this incompatibility is discussed.
Complex-energy approach to sum rules within nuclear density functional theory
NASA Astrophysics Data System (ADS)
Hinohara, Nobuo; Kortelainen, Markus; Nazarewicz, Witold; Olsen, Erik
2015-04-01
Background: The linear response of the nucleus to an external field contains unique information about the effective interaction, the correlations governing the behavior of the many-body system, and the properties of its excited states. To characterize the response, it is useful to use its energy-weighted moments, or sum rules. By comparing computed sum rules with experimental values, the information content of the response can be utilized in the optimization process of the nuclear Hamiltonian or the nuclear energy density functional (EDF). But the additional information comes at a price: compared to the ground state, computation of excited states is more demanding. Purpose: To establish an efficient framework to compute energy-weighted sum rules of the response that is adaptable to the optimization of the nuclear EDF and large-scale surveys of collective strength, we have developed a new technique within the complex-energy finite-amplitude method (FAM) based on the quasiparticle random-phase approximation (QRPA). Methods: To compute sum rules, we carry out contour integration of the response function in the complex-energy plane. We benchmark our results against the conventional matrix formulation of the QRPA theory, the Thouless theorem for the energy-weighted sum rule, and the dielectric theorem for the inverse-energy-weighted sum rule. Results: We derive the sum-rule expressions from the contour integration of the complex-energy FAM. We demonstrate that calculated sum-rule values agree with those obtained from the matrix formulation of the QRPA. We also discuss the applicability of both the Thouless theorem about the energy-weighted sum rule and the dielectric theorem for the inverse-energy-weighted sum rule to nuclear density functional theory in cases when the EDF is not based on a Hamiltonian. Conclusions: The proposed sum-rule technique based on the complex-energy FAM is a tool of choice when optimizing effective interactions or energy functionals. The method
Modified Kramers-Kronig relations and sum rules for meromorphic total refractive index
Peiponen, Kai-Erik; Saarinen, Jarkko J.; Vartiainen, Erik M.
2003-08-01
Modified Kramers-Kronig relations and corresponding sum rules are shown to hold for the total refractive index that can be presented as a sum of complex linear and nonlinear refractive indices, respectively. It is suggested that a self-action process, involving the degenerate third-order nonlinear susceptibility, can yield a negative total refractive index at some spectral range.
Experimental Tests of the GDH and Other Sum Rules at SLAC
Bosted, P.E.; /Massachusetts U., Amherst
2005-06-14
Recent measurements from SLAC of the polarized nucleon structure functions g{sub 1} and g{sub 2} have been used to experimentally test the Bjorken, Ellis-Jaffe, Burkhardt-Cottingham, and Efremov-Leader-Teryaev sum rules. In the future, the SLAC E159 experiment will extend structure function measurements using real photons to 40 GeV, enabling a definitive test of the high energy convergence of the GDH sum rule for both proton and deuteron targets.
QCD sum rules for magnetically induced mixing between ηc and J/ψ.
Cho, Sungtae; Hattori, Koichi; Lee, Su Houng; Morita, Kenji; Ozaki, Sho
2014-10-24
We investigate the properties of charmonia in strong magnetic fields by using QCD sum rules. We show how to implement the mixing effects between η(c) and J/ψ on the basis of field-theoretical approaches, and then show that the sum rules are saturated by the mixing effects with phenomenologically determined parameters. Consequently, we find that the mixing effects are the dominant contribution to the mass shifts of the static charmonia in strong magnetic fields.
QCD Sum Rules for Magnetically Induced Mixing between ηc and J/ψ
Cho, Sungtae; Hattori, Koichi; Lee, Su Houng; ...
2014-10-20
We investigate the properties of charmonia in strong magnetic fields by using QCD sum rules. We show how to implement the mixing effects between ηc and J/ψ on the basis of field-theoretical approaches, and then show that the sum rules are saturated by the mixing effects with phenomenologically determined parameters. Consequently, we find that the mixing effects are the dominant contribution to the mass shifts of the static charmonia in strong magnetic fields.
QCD Sum Rules for Magnetically Induced Mixing between ηc and J/ψ
Cho, Sungtae; Hattori, Koichi; Lee, Su Houng; Morita, Kenji; Ozaki, Sho
2014-10-20
We investigate the properties of charmonia in strong magnetic fields by using QCD sum rules. We show how to implement the mixing effects between ηc and J/ψ on the basis of field-theoretical approaches, and then show that the sum rules are saturated by the mixing effects with phenomenologically determined parameters. Consequently, we find that the mixing effects are the dominant contribution to the mass shifts of the static charmonia in strong magnetic fields.
Sum Rules of Charm CP Asymmetries beyond the SU(3)_{F} Limit.
Müller, Sarah; Nierste, Ulrich; Schacht, Stefan
2015-12-18
We find new sum rules between direct CP asymmetries in D meson decays with coefficients that can be determined from a global fit to branching ratio data. Our sum rules eliminate the penguin topologies P and PA, which cannot be determined from branching ratios. In this way, we can make predictions about direct CP asymmetries in the standard model without ad hoc assumptions on the sizes of penguin diagrams. We consistently include first-order SU(3)_{F} breaking in the topological amplitudes extracted from the branching ratios. By confronting our sum rules with future precise data from LHCb and Belle II, one will identify or constrain new-physics contributions to P or PA. The first sum rule correlates the CP asymmetries a_{CP}^{dir} in D^{0}→K^{+}K^{-}, D^{0}→π^{+}π^{-}, and D^{0}→π^{0}π^{0}. We study the region of the a_{CP}^{dir}(D^{0}→π^{+}π^{-})-a_{CP}^{dir}(D^{0}→π^{0}π^{0}) plane allowed by current data and find that our sum rule excludes more than half of the allowed region at 95% C.L. Our second sum rule correlates the direct CP asymmetries in D^{+}→K[over ¯]^{0}K^{+}, D_{s}^{+}→K^{0}π^{+}, and D_{s}^{+}→K^{+}π^{0}.
Sum Rules of Charm C P Asymmetries beyond the SU(3 ) F Limit
NASA Astrophysics Data System (ADS)
Müller, Sarah; Nierste, Ulrich; Schacht, Stefan
2015-12-01
We find new sum rules between direct C P asymmetries in D meson decays with coefficients that can be determined from a global fit to branching ratio data. Our sum rules eliminate the penguin topologies P and P A , which cannot be determined from branching ratios. In this way, we can make predictions about direct C P asymmetries in the standard model without ad hoc assumptions on the sizes of penguin diagrams. We consistently include first-order SU(3 ) F breaking in the topological amplitudes extracted from the branching ratios. By confronting our sum rules with future precise data from LHCb and Belle II, one will identify or constrain new-physics contributions to P or P A . The first sum rule correlates the C P asymmetries aCP dir in D0→K+K-, D0→π+π- , and D0→π0π0. We study the region of the aCP dir(D0→π+π-)-aCP dir(D0→π0π0) plane allowed by current data and find that our sum rule excludes more than half of the allowed region at 95% C.L. Our second sum rule correlates the direct C P asymmetries in D+→K¯0K+, Ds+→K0π+, and Ds+→K+π0.
van der Waals forces, sum rules, and pseudostate expansions
NASA Astrophysics Data System (ADS)
Au, C. K.; Drachman, Richard J.
1988-02-01
We reexamine the pseudostate expansion used previously to evaluate van der Waals (vdW) coefficients and finite-mass corrections. In particular, we wish to understand the very rapid convergence of the expansion, which for the case of two hydrogenic atoms requires only ten terms to achieve an accuracy of 1×10-10. The analysis proceeds from the representation of the vdW coefficients as integrals of single-atom frequency-dependent polarizabilities. These in turn can be expanded in power series with coefficients of the form JnM2(nl)/(Enl-E1s)k, where M(nl) is a multipole matrix element between the ground (1s) and excited (nl) states. Although defined as sums over an infinite set of hydrogenic states, the coefficients of each order k are reproduced exactly by a finite sum over suitable pseudostates. By analytic continuation, the frequency-dependent polarizabilities computed using pseudostates are expected to be very close to the exact values, and hence the rapid convergence of the vdW coefficients is understood.
QCD sum rules for the neutron, Σ , and Λ in neutron matter
NASA Astrophysics Data System (ADS)
Jeong, Kie Sang; Gye, Giju; Lee, Su Houng
2016-12-01
The nuclear density dependencies of the neutron and Σ and Λ hyperons are important inputs in the determination of the neutron star mass as the appearance of hyperons coming from strong attractions significantly changes the stiffness of the equation of state (EOS) at iso-spin asymmetric dense nuclear matter. In-medium spectral sum rules have been analyzed for the nucleon, Σ , and Λ hyperon to investigate their properties up to slightly above the saturation nuclear matter density by using the linear density approximation for the condensates. The construction scheme of the interpolating fields without derivatives has been reviewed and used to construct a general interpolating field for each baryon with parameters specifying the strength of independent interpolating fields. Optimal choices for the interpolating fields were obtained by requiring the sum rules to be stable against variations of the parameters and the result to be consistent with known phenomenology. The optimized result shows that Ioffe's choice is not suitable for the Λ hyperon sum rules. It is found that, for the Λ hyperon interpolating field, the up and down quark combined into the scalar diquark structure uTC γ5d should be emphasized to ensure stable sum rules. The quasi-Σ and -Λ hyperon energies are always found to be higher than the quasineutron energy in the region 0.5 <ρ /ρ0<1.5 where the linear density approximation in the sum-rule analysis is expected to be reliable.
Finite temperature effects and the validity of the Weinberg sum rules
NASA Astrophysics Data System (ADS)
Ayala, Alejandro; Dominguez, C. A.; Loewe, M.; Zhang, Y.
2016-05-01
Using resent independent results from QCD sum rules for the thermal evolution of hadronic parameters in the vector and the axial-vector channels, we discuss the saturation of the two Weinberg sum rules. It turn out that both sum rules are quite well satisfied in a wide range from T = 0 up to T/T c ≃ 0.7 — 0.8. At higher temperatures, coming closer to Tc , there is an asymmetry between both channels since in the vector case there is a leading order effect, proportional to T2 , due to a one loop pion contribution in the space-like region, which is absent in the axial-vector case. This leads then to a small deviation. More important, though, in this region the QCD sum rules for the hadronic parameters begin to have no solutions since the widths of the ρ and the a1-mesons diverge signaling the occurrence of deconfinement. Close to and at Tc there are no pions left in the medium and chiral symmetry is restored so that the Weinberg sum rules are trivially satisfied.
Spin structure of the neutron ({sup 3}He) and the Bjoerken sum rule
Meziani, Z.E.; E-142 Collaboration
1994-02-01
A first measurement of the longitudinal asymmetry of deepinelastic scattering of Polarized electrons from a Polarized {sup 3}He target at energies ranging from 19 to 26 GeV ha, been performed at the Stanford Linear Accelerator Center (SLAC). The spin-Structure function of the neutron g{sub 1}{sup n} has been extracted from the measured asymmetries. The Quark Parton Model (QPM) interpretation of the nucleon spin-structure function is examined in light of the new results. A test of the Ellis-Jaffe sum rule (E-J) on the neutron is performed at high momentum transfer and found to be satisfied. Furthermore, combining the proton results of European Muon Collaboration (EMC) and the neutron results of E-142 the Bjoerken sum rule test is carried at high Q{sup 2} where higher order Perturbative Quantum Chromodynamics (PQCD) corrections and higher-twist corrections are smaller. The sum rule saturated to within one standard deviation.
Thermal behaviors of light unflavored tensor mesons in the framework of QCD sum rule
NASA Astrophysics Data System (ADS)
Azizi, K.; Türkan, A.; Sundu, H.; Veli Veliev, E.; Yazıcı, E.
2014-12-01
In this paper, we investigated the sensitivity of the masses and decay constants of f2(1270) and a2(1320) tensor mesons to the temperature using OCD sum rule approach. In our calculations, we take into account new additional operators appearing in operator product expansion (OPE). At the end of numerical analyses we show that at deconfinement temperature the decay constants and masses decreased by 6% and 96% of their vacuum values, respectively. Our results on the masses and decay constants at zero temperature of the tensor mesons are consistent with the experimental data as well as the vacuum sum rules predictions.
Light Cone Sum Rules for gamma*N ->Delta Transition Form Factors
V.M. Braun; A. Lenz; G. Peters; A. Radyushkin
2006-02-01
A theoretical framework is suggested for the calculation of {gamma}* N {yields} {Delta} transition form factors using the light-cone sum rule approach. Leading-order sum rules are derived and compared with the existing experimental data. We find that the transition form factors in a several GeV region are dominated by the ''soft'' contributions that can be thought of as overlap integrals of the valence components of the hadron wave functions. The ''minus'' components of the quark fields contribute significantly to the result, which can be reinterpreted as large contributions of the quark orbital angular momentum.
Measurement of the neutron spin structure function---Test of the Bjorken sum rule
Petratos, G.G.
1991-08-01
As experiment to measure the neutron spin-dependent structure function g{sub 1}{sup n} (x) over a range in x from 0.04 to 0.7 and with Q{sup 2} > 1 (GeV/c){sup 2} is presented. The experiment consists of scattering a longitudinally polarized electron beam from the Stanford Linear Accelerator off a polarized {sup 3}He target and detecting scattered electrons in two magnetic spectrometers. The experiment will provide a critical test of the Bjorken sum rule and valuable information in understanding the nucleon spin structure and the violation of the Ellis-Jaffe sum rule. 3 figs., 1 tab.
Spin-dependent sum rules connecting real and virtual Compton scattering verified
NASA Astrophysics Data System (ADS)
Lensky, Vadim; Pascalutsa, Vladimir; Vanderhaeghen, Marc; Kao, Chung Wen
2017-04-01
We present a detailed derivation of the two sum rules relating the spin polarizabilities measured in real, virtual, and doubly virtual Compton scattering. For example, the polarizability δL T , accessed in inclusive electron scattering, is related to the spin polarizability γE 1 E 1 and the slope of generalized polarizabilities P(M 1 ,M 1 )1-P(L 1 ,L 1 )1 , measured in, respectively, the real and the virtual Compton scattering. We verify these sum rules in different variants of chiral perturbation theory, discuss their empirical verification for the proton, and prospect their use in studies of the nucleon spin structure.
Iso-vector form factors of the delta and nucleon in QCD sum rules
Ozpineci, A.
2012-10-23
Form factors are important non-perturbative properties of hadrons. They give information about the internal structure of the hadrons. In this work, iso-vector axial-vector and iso-vector tensor form factors of the nucleon and the iso-vector axial-vector {Delta}{yields}N transition form factor calculations in QCD Sum Rules are presented.
{kappa}K*{sup 0}{gamma}-vertex in light cone QCD sum rules
Gokalp, A.; Yilmaz, O.; Sarac, Y.
2008-06-01
We investigate the {kappa}K*{sup 0}{gamma}-vertex in the framework of light cone QCD sum rules. We estimate the coupling constant g{sub {kappa}}{sub K*{sup 0}}{sub {gamma}}, and compare our result with that used in the nonlinear chiral Lagrangian approach using the vector-meson dominance model in the SU(3) limit.
Complex-energy approach to sum rules within nuclear density functional theory
Hinohara, Nobuo; Kortelainen, Markus; Nazarewicz, Witold; ...
2015-04-27
The linear response of the nucleus to an external field contains unique information about the effective interaction, correlations governing the behavior of the many-body system, and properties of its excited states. To characterize the response, it is useful to use its energy-weighted moments, or sum rules. By comparing computed sum rules with experimental values, the information content of the response can be utilized in the optimization process of the nuclear Hamiltonian or nuclear energy density functional (EDF). But the additional information comes at a price: compared to the ground state, computation of excited states is more demanding. To establish anmore » efficient framework to compute energy-weighted sum rules of the response that is adaptable to the optimization of the nuclear EDF and large-scale surveys of collective strength, we have developed a new technique within the complex-energy finite-amplitude method (FAM) based on the quasiparticle random- phase approximation. The proposed sum-rule technique based on the complex-energy FAM is a tool of choice when optimizing effective interactions or energy functionals. The method is very efficient and well-adaptable to parallel computing. As a result, the FAM formulation is especially useful when standard theorems based on commutation relations involving the nuclear Hamiltonian and external field cannot be used.« less
Analysis of the Y(4220) and Y(4390) as molecular states with QCD sum rules
NASA Astrophysics Data System (ADS)
Wang, Zhi-Gang
2017-08-01
In this article, we assign the Y(4390) and Y(4220) to be the vector molecular states DD¯1 (2420) and , respectively, and study their masses and pole residues in detail with the QCD sum rules. The present calculations only favor assigning the Y(4390) to be the DD¯1(1- -) molecular state. Supported by National Natural Science Foundation (11375063)
Complex-energy approach to sum rules within nuclear density functional theory
Hinohara, Nobuo; Kortelainen, Markus; Nazarewicz, Witold; Olsen, Erik
2015-04-27
The linear response of the nucleus to an external field contains unique information about the effective interaction, correlations governing the behavior of the many-body system, and properties of its excited states. To characterize the response, it is useful to use its energy-weighted moments, or sum rules. By comparing computed sum rules with experimental values, the information content of the response can be utilized in the optimization process of the nuclear Hamiltonian or nuclear energy density functional (EDF). But the additional information comes at a price: compared to the ground state, computation of excited states is more demanding. To establish an efficient framework to compute energy-weighted sum rules of the response that is adaptable to the optimization of the nuclear EDF and large-scale surveys of collective strength, we have developed a new technique within the complex-energy finite-amplitude method (FAM) based on the quasiparticle random- phase approximation. The proposed sum-rule technique based on the complex-energy FAM is a tool of choice when optimizing effective interactions or energy functionals. The method is very efficient and well-adaptable to parallel computing. As a result, the FAM formulation is especially useful when standard theorems based on commutation relations involving the nuclear Hamiltonian and external field cannot be used.
Light-by-light scattering sum rules in light of new data
NASA Astrophysics Data System (ADS)
Danilkin, Igor; Vanderhaeghen, Marc
2017-01-01
We evaluate the light-quark meson contributions to three exact light-by-light scattering sum rules in light of new data by the Belle Collaboration, which recently has extracted the transition form factors of the tensor meson f2(1270 ) as well as of the scalar meson f0(980 ). We confirm a previous finding that the η ,η' and helicity-2 f2(1270 ) contributions saturate one of these sum rules up to photon virtualities around 1 Ge V2 . At larger virtualities, our sum rule analysis shows an important contribution of the f2(1565 ) meson and provides a first empirical extraction of its helicity-2 transition form factor. Two further sum rules allow us to predict the helicity-0 and helicity-1 transition form factors of the f2(1270 ) meson. Furthermore, our analysis also provides an update for the scalar and tensor meson hadronic light-by-light contributions to the muon's anomalous magnetic moment.
Sum rule distortions in fluorescence-yield x-ray magnetic circular dichroism
NASA Astrophysics Data System (ADS)
Liu, Boyang; Piamonteze, Cinthia; Delgado-Jaime, Mario Ulises; Wang, Ru-Pan; Heidler, Jakoba; Dreiser, Jan; Chopdekar, Rajesh; Nolting, Frithjof; de Groot, Frank M. F.
2017-08-01
The quantitative analysis of 3 d transition metal L2 ,3 edge x-ray magnetic circular dichroism (XMCD) spectra and the related sum rules are compared for measurements with electron yield and fluorescence yield detection. Multiplet calculations on divalent ions show that fluorescence yield detected sum rule derived expectation values of Lz and Sz show noticeable deviations and detection angle dependence. We show that small deviations of the polarization dependent fluorescent decay values lead to significant deviations in the Lz and Sz sum rule values. Fe and Co experimental XMCD spectra of a supported 10 nm CoFe2O4 thin film are measured simultaneously by both electron and fluorescence yield. The deviations shown in the experimental data are well explained by the calculations and are shown to mainly depend on the polarization dependent total decay. We conclude that fluorescence yield detected x-ray magnetic circular dichroism is unsuitable for quantitative analysis of the Lz and Sz sum rule values.
An inspection on the Borel masses relation used in QCD sum rules
Osorio Rodrigues, B.; Chiapparini, M.; Bracco, M. E.
2010-11-12
In this work, we studied the Borel masses relation used in QCD Sum Rules (QCDSR) calculations. These masses are the parameters of the Borel transform used when the three point function is calculated. We analised an usual and a more general linear relations. We concluded that a general linear relation between these masses provides the best results regarding the standard deviation.
A comprehensive revisit of the ρ meson with improved Monte-Carlo based QCD sum rules
NASA Astrophysics Data System (ADS)
Wang, Qi-Nan; Zhang, Zhu-Feng; Steele, T. G.; Jin, Hong-Ying; Huang, Zhuo-Ran
2017-07-01
We improve the Monte-Carlo based QCD sum rules by introducing the rigorous Hölder-inequality-determined sum rule window and a Breit-Wigner type parametrization for the phenomenological spectral function. In this improved sum rule analysis methodology, the sum rule analysis window can be determined without any assumptions on OPE convergence or the QCD continuum. Therefore, an unbiased prediction can be obtained for the phenomenological parameters (the hadronic mass and width etc.). We test the new approach in the ρ meson channel with re-examination and inclusion of α s corrections to dimension-4 condensates in the OPE. We obtain results highly consistent with experimental values. We also discuss the possible extension of this method to some other channels. Supported by NSFC (11175153, 11205093, 11347020), Open Foundation of the Most Important Subjects of Zhejiang Province, and K. C. Wong Magna Fund in Ningbo University, TGS is Supported by the Natural Sciences and Engineering Research Council of Canada (NSERC), Z. F. Zhang and Z. R. Huang are Grateful to the University of Saskatchewan for its Warm Hospitality
Light-cone Sum Rules in Soft-Collinear Effective Theory
De Fazio, Fulvia; Feldmann, Thorsten; Hurth, Tobias; /CERN /SLAC
2005-06-20
We derive light-cone sum rules (LCSRs) for exclusive B-meson decays into light energetic hadrons from correlation functions within soft-collinear effective theory (SCET). In these sum rules the short-distance scale refers to ''hard-collinear'' interactions with virtualities of order {Lambda}{sub QCD}m{sub b}. Hard scales (related to virtualities of order m{sub b}{sup 2}) are integrated out and enter via external coefficient functions in the sum rule. Soft dynamics is encoded in light-cone distribution amplitudes for the B-meson, which describe both the factorizable and non-factorizable contributions to exclusive B-meson decay amplitudes. As an example, we provide a detailed study of the SCET sum rule for the B {yields} {pi} transition form factor at large recoil, including radiative corrections from hard-collinear loop diagrams at first order in the strong coupling constant. We find remarkable conceptual and numerical differences with the heavy-quark limit of the conventional LCSR approach in QCD.
A Measurement of $\\alpha_s$ from the Gross-Llewellyn Smith sum rule
Kim, John Hanju
1998-01-01
A set of values for the Gross-Llewellyn Smith sum rule are extracted at different values of 4-momentum transfer squared (Q^{2}), by combining revised CCFR neutrino data with data from other neutrino deep-inelastic scattering experiments for 1 2 < 15 GeV^{2}/ c^{2}.
Maple procedures for the coupling of angular momenta II. Sum rule evaluation
NASA Astrophysics Data System (ADS)
Fritzsche, S.; Varga, S.; Geschke, D.; Fricke, B.
1998-06-01
In a previous paper (S. Fritzsche, Comput. Phys. Commun. 103 (1997) 51), we defined data structures to deal with typical expressions from Racah algebra within the framework of Maple. Such expressions arise very frequently in various fields, for instance, by treating composite wave functions and tensor operators in many-particle physics. Often, these Racah expressions are written in terms of Clebsch-Gordan coefficients and Wigner n-j symbols. Our previous set of Maple procedures mainly concerned numerical computations on such symbols, the simplification by special values as well as the use of recursion relations. The full elegance of applying Racah algebra techniques in daily research work is, however, only revealed by the analytic simplification of more complex expressions. In practise, this even requires the major effort in dealing with these techniques. Its success closely depends on the knowledge of sum rules which typically include a number of dummy summation indices. The application of these sum rules is a rather straightforward task but may become very tedious for more difficult expressions due to the large number of symmetries of the Clebsch-Gordan coefficients and Wigner n-j symbols. We therefore extended the Racah program to facilitate sum rule evaluations in the given framework. A set of new and revised procedures now supports the evaluation of Racah algebra expressions by applying the orthogonality properties of the Wigner symbols and a variety of sum rules. More than 40 sum rules known from the literature and involving products of up to six Wigner n-j symbols have been implemented and are available for interactive use. The applicability of this new tool will be demonstrated by three examples from many-particle physics.
Nambu sum rule and the relation between the masses of composite Higgs bosons
NASA Astrophysics Data System (ADS)
Volovik, G. E.; Zubkov, M. A.
2013-04-01
We review the known results on the bosonic spectrum in various Nambu-Jona-Lasinio models both in condensed matter physics and in relativistic quantum field theory including He3-B, He3-A, the thin films of superfluid He3, and QCD (Hadronic phase and the color-flavor locking phase). Next, we calculate the bosonic spectrum in the relativistic model of top quark condensation suggested in [Phys. Lett. B 221, 177 (1989)PYLBAJ0370-269310.1016/0370-2693(89)91494-9]. In all considered cases, the sum rule appears, which relates the masses (energy gaps) Mboson of the bosonic excitations in each channel with the mass (energy gap) of the condensed fermion Mf as ∑Mboson2=4Mf2. Previously, this relation was established by Nambu for He3-B and for the s-wave superconductor. We generalize this relation to the wider class of models and call it the Nambu sum rule. We discuss the possibility to apply this sum rule to various models of top quark condensation. In some cases, this rule allows us to calculate the masses of extra Higgs bosons that are the Nambu partners of the 125 GeV Higgs.
Superscaling analysis of the Coulomb sum rule in quasielastic electron-nucleus scattering
NASA Astrophysics Data System (ADS)
Caballero, J. A.; Martínez, M. C.; Herraíz, J. L.; Udías, J. M.
2010-05-01
The Coulomb sum rule for inclusive quasielastic electron scattering in 12C, 40Ca and 56Fe is analyzed based on scaling and superscaling properties. Results obtained in the relativistic impulse approximation with various descriptions of the final state interactions are shown. A comparison with experimental data measured at Bates and Saclay is provided. The theoretical description based on strong scalar and vector terms present in the relativistic mean field, which has been shown to reproduce the experimental asymmetric superscaling function, leads to results that are in fair agreement with Bates data while it sizeably overestimates Saclay data. We find that the Coulomb sum rule for a momentum transfer q ⩾ 500 MeV / c saturates to a value close to 0.9, being very similar for the three nuclear systems considered. This is in accordance with Bates data, which indicates that these show no significative quenching in the longitudinal response.
Experimental Check of the Gerasimov-Drell-Hearn Sum Rule for 1H
NASA Astrophysics Data System (ADS)
Dutz, H.; Helbing, K.; Krimmer, J.; Speckner, T.; Zeitler, G.; Ahrens, J.; Altieri, S.; Annand, J. R.; Anton, G.; Arends, H.-J.; Beck, R.; Bock, A.; Bradtke, C.; Braghieri, A.; v. Drachenfels, W.; Frommberger, F.; Godo, M.; Goertz, S.; Grabmayr, P.; Hasegawa, S.; Hansen, K.; Harmsen, J.; Heid, E.; Hillert, W.; Holvoet, H.; Horikawa, N.; Iwata, T.; Hoorebeke, L. Van; D'Hose, N.; Jennewein, P.; Kiel, B.; Klein, F.; Kondratiev, R.; Lang, M.; Lannoy, B.; Leukel, R.; Lisin, V.; Menze, D.; Meyer, W.; Michel, T.; Naumann, J.; Panzeri, A.; Pedroni, P.; Pinelli, T.; Preobrajenski, I.; Radtke, E.; Reicherz, G.; Rohlof, C.; Rostomyan, T.; Sauer, M.; Schoch, B.; Schumacher, M.; Tamas, G.; Thomas, A.; van de Vyver, R.; Weihofen, W.; Zapadtka, F.
2004-07-01
For the first time we checked the fundamental Gerasimov-Drell-Hearn (GDH) sum rule for the proton experimentally in the photon energy range from 0.2 2.9GeV with the tagged photon facilities at MAMI (Mainz) and ELSA (Bonn). New data of the doubly polarized total cross section difference are presented in the energy range from 1.6 to 2.9GeV. The contribution to the GDH integral from 0.2 2.9GeV yields [254±5(stat)±12(syst)] μb with negative contributions in the Regge regime at photon energies above 2.1GeV. This trend supports the validity of the GDH sum rule.
A QCD Sum Rule Approach with an Explicit Di-quark field
Kim, Kyung-il; Jido, Daisuke; Lee, Su Houng
2011-10-21
In hadron phenomenology, diquark structures can be an important degree of freedom in certain configurations. We investigate the possibility that the diquark structure can be treated as an elementary field in certain configurations. To start with, we assume that {Lambda} is composed of a spectator strange quark and a diquark. We construct a QCD sum rule for {Lambda}, where the input parameters are the diquark mass and its condensate, in addition to other parameters of QCD sum rules. We find good Borel curve for the {Lambda} mass for certain combinations of the diquark mass and condensate, and that smaller diquark condensate is needed when the diquark mass is increased to maintain the good Borel curve. The same sets of diquark mass and condensate are found to work well for {Lambda}{sub c} and {Lambda}{sub b}.
An exact sum-rule for the Hubbard model: an historical/pedagogical approach
NASA Astrophysics Data System (ADS)
Di Matteo, S.; Claveau, Y.
2017-07-01
The aim of the present article is to derive an exact integral equation for the Green function of the Hubbard model through an equation-of-motion procedure, like in the original Hubbard papers. Though our exact integral equation does not allow to solve the Hubbard model, it represents a strong constraint on its approximate solutions. An analogous sum rule has been already obtained in the literature, through the use of a spectral moment technique. We think however that our equation-of-motion procedure can be more easily related to the historical procedure of the original Hubbard papers. We also discuss examples of possible applications of the sum rule and propose and analyse a solution, fulfilling it, that can be used for a pedagogical introduction to the Mott-Hubbard metal-insulator transition.
Strength function sum rules and the generalized Brink-Axel hypothesis
NASA Astrophysics Data System (ADS)
Johnson, Calvin W.
2015-10-01
Sum rules provide useful insights into transition strength functions and are often expressed as expectation values of an operator. I will show that non-energy-weighted transition sum rules have strong secular dependences on the energy of the initial state. Such non-trivial systematics have consequences: the simplification suggested by the generalized Brink-Axel hypothesis, for example, does not hold for most cases, though it weakly holds for electric dipole transitions. Furthermore, I show the systematics can be understood through spectral distribution theory, calculated via traces of operators and of products of operators; seen through this lens, violation of the generalized Brink-Axel hypothesis is unsurprising. Supported by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics, under Award Number DE-FG02-96ER40985.
Octet magnetic moments and the Coleman-Glashow sum rule violation in the chiral quark model
NASA Astrophysics Data System (ADS)
Dahiya, Harleen; Gupta, Manmohan
2002-09-01
Baryon octet magnetic moments when calculated within the chiral quark model, incorporating the orbital angular momentum as well as the quark sea contribution through the Cheng-Li mechanism, not only show improvement over the nonrelativistic quark model results but also give a nonzero value for the right-hand side of the Coleman-Glashow sum rule. When effects due to spin-spin forces between constituent quarks as well as ``mass adjustments'' due to confinement are added, it leads to an excellent fit for the case of p,Σ+, Ξo and violation of the Coleman-Glashow sum rule, whereas in almost all the other cases the results are within 5% of the data.
STrM/sup 2/ sum rule for a general class of Kahler potentials
Chang, N.P.; Leon, J.; Mercader, J.P.
1987-12-01
The authors study the sum rule for the mass squared of the N = 1 four dimensional effective supersymmetric theory whose Kahler potential is of the general form that appears in compactified superstrings. They take full account of the non-minimal nature of the models. They discuss the conditions under which one can have both a vanishing cosmological constant and a zero STrM/sup 2/.
Dibaryon octet strong decay coupling constants sum rules with first-order SU(3) symmetry breaking
NASA Astrophysics Data System (ADS)
Polanco-Euán, E. N.; Sánchez-Colón, G.; Gupta, V.
2017-03-01
The SU(3) octet states with baryon number B = 2, hexaquark dibaryons, are considered. We extend previous work and determine strong decay coupling constants sum rules with first-order SU(3) symmetry breaking for dibaryon octet into two ordinary baryon octets and into a baryon octet plus a baryon decuplet. Possibilities for the experimental observation of multibaryon and anti-multibaryon states are pointed out.
Model calculations of the Sivers function satisfying the Burkardt sum rule
Courtoy, A.; Vento, V.; Scopetta, S.
2009-04-01
It is shown that, at variance with previous analyses, the MIT bag model can explain the available data of the Sivers function and satisfies the Burkardt sum rule to a few percent accuracy. The agreement is similar to the one recently found in the constituent quark model. Therefore, these two model calculations of the Sivers function are in agreement with the present experimental and theoretical wisdom.
Analysis of X(1576) as a Tetraquark State with the QCD Sum Rules
NASA Astrophysics Data System (ADS)
Wang, Zhi-Gang; Wan, Shao-Long
2006-12-01
We take the viewpoint that X(1576) is the tetraquark state which consists of a scalar diquark and an anti-scalar-diquark in relative P-wave, and calculate its mass in the framework of the QCD sum rule approach. The numerical value of the mass mX = (1.66±0.14) GeV is consistent with the experimental data. There might be some tetraquark components in the vector meson X(1576).
Heavy-Quark Mass and Heavy-Meson Decay Constants from QCD Sum Rules
Lucha, Wolfgang; Melikhov, Dmitri; Simula, Silvano
2011-05-23
We present a sum-rule extraction of decay constants of heavy mesons from the two-point correlator of heavy-light pseudoscalar currents. Our primary concern is to control the uncertainties of the decay constants, induced by both input QCD parameters and limited accuracy of the sum-rule method. Gaining this control is possible by applying our novel procedure for the extraction of hadron observables utilizing Borel-parameter-depending dual thresholds. For the charmed mesons, we obtain f{sub D} (206.2{+-}7.3{sub (OPE){+-}}5.1{sub (syst)}) MeV and f{sub D{sub s}} (245.3{+-}15.7{sub (OPE){+-}}4.5{sub (syst)}) MeV. In the case of the beauty mesons, the decay constants prove to be extremely sensitive to the exact value of the b-quark MS mass m-bar{sub b}(m-bar{sub b}). By matching our sum-rule prediction for f{sub B} to the lattice outcomes, the very accurate b-mass value m-bar{sub b}(m-bar{sub b}) = (4.245{+-}0.025) GeV is found, which yields f{sub B} = (193.4{+-}12.3{sub (OPE){+-}}4.3{sub (syst)}) MeV and f{sub B{sub s}} (232.5{+-}18.6{sub (OPE){+-}}2.4{sub (syst)}) MeV.
Ultrafast zero balance of the oscillator-strength sum rule in graphene
Kim, Jaeseok; Lim, Seong Chu; Chae, Seung Jin; Maeng, Inhee; Choi, Younghwan; Cha, Soonyoung; Lee, Young Hee; Choi, Hyunyong
2013-01-01
Oscillator-strength sum rule in light-induced transitions is one general form of quantum-mechanical identities. Although this sum rule is well established in equilibrium photo-physics, an experimental corroboration for the validation of the sum rule in a nonequilibrium regime has been a long-standing unexplored question. The simple band structure of graphene is an ideal system for investigating this question due to the linear Dirac-like energy dispersion. Here, we employed both ultrafast terahertz and optical spectroscopy to directly monitor the transient oscillator-strength balancing between quasi-free low-energy oscillators and high-energy Fermi-edge ones. Upon photo-excitation of hot Dirac fermions, we observed that the ultrafast depletion of high-energy oscillators precisely complements the increased terahertz absorption oscillators. Our results may provide an experimental priori to understand, for example, the intrinsic free-carrier dynamics to the high-energy photo-excitation, responsible for optoelectronic operation such as graphene-based phototransistor or solar-energy harvesting devices. PMID:24036567
Nature of the X(5568) — A critical Laplace sum rule analysis at N2LO
NASA Astrophysics Data System (ADS)
Albuquerque, R.; Narison, S.; Rabemananjara, A.; Rabetiarivony, D.
2016-06-01
We scrutinize recent QCD spectral sum rules (QSSR) results to lowest order (LO) predicting the masses of the BK molecule and (su)(bd¯) four-quark states. We improve these results by adding NLO and N2LO corrections to the PT contributions giving a more precise meaning on the b-quark mass definition used in the analysis. We extract our optimal predictions using Laplace sum rule (LSR) within the standard stability criteria versus the changes of the external free parameters (τ-sum rule variable, tc continuum threshold and subtraction constant μ). The smallness of the higher order PT corrections justifies (a posteriori) the LO order results ⊕ the uses of the ambiguous heavy quark mass to that order. However, our predicted spectra in the range (5173 ˜ 5226) MeV, summarized in Table 7, for exotic hadrons built with four different flavors (buds), do not support some previous interpretations of the D0 candidate,1 X(5568), as a pure molecule or a four-quark state. If experimentally confirmed, it could result from their mixing with an angle: sin 2𝜃 ≈ 0.15. One can also scan the region (2327 ˜ 2444) MeV (where the Ds0∗(2317) might be a good candidate) and the one (5173 ˜ 5226) MeV for detecting these (cuds) and (buds) unmixed exotic hadrons (if any) via, eventually, their radiative or π+hadrons decays.
Spin structure of the neutron ({sup 3}He) and the Bjoerken sum rule
Meziani, Z.E.
1994-12-01
A first measurement of the longitudinal asymmetry of deep-inelastic scattering of polarized electrons from a polarized {sup 3}He target at energies ranging from 19 to 26 GeV has been performed at the Stanford Linear Accelerator Center (SLAC). The spin-structure function of the neutron g{sub 1}{sup n} has been extracted from the measured asymmetries. The Quark Parton Model (QPM) interpretation of the nucleon spin-structure function is examined in light of the new results. A test of the Ellis-Jaffe sum rule (E-J) on the neutron is performed at high momentum transfer and found to be satisfied. Furthermore, combining the proton results of the European Muon Collaboration (EMC) and the neutron results of E-142, the Bjoerken sum rule test is carried at high Q{sup 2} where higher order Perturbative Quantum Chromodynamics (PQCD) corrections and higher-twist corrections are smaller. The sum rule is saturated to within one standard deviation.
Ultrafast zero balance of the oscillator-strength sum rule in graphene.
Kim, Jaeseok; Lim, Seong Chu; Chae, Seung Jin; Maeng, Inhee; Choi, Younghwan; Cha, Soonyoung; Lee, Young Hee; Choi, Hyunyong
2013-01-01
Oscillator-strength sum rule in light-induced transitions is one general form of quantum-mechanical identities. Although this sum rule is well established in equilibrium photo-physics, an experimental corroboration for the validation of the sum rule in a nonequilibrium regime has been a long-standing unexplored question. The simple band structure of graphene is an ideal system for investigating this question due to the linear Dirac-like energy dispersion. Here, we employed both ultrafast terahertz and optical spectroscopy to directly monitor the transient oscillator-strength balancing between quasi-free low-energy oscillators and high-energy Fermi-edge ones. Upon photo-excitation of hot Dirac fermions, we observed that the ultrafast depletion of high-energy oscillators precisely complements the increased terahertz absorption oscillators. Our results may provide an experimental priori to understand, for example, the intrinsic free-carrier dynamics to the high-energy photo-excitation, responsible for optoelectronic operation such as graphene-based phototransistor or solar-energy harvesting devices.
Fourth Moment Sum Rule for the Charge Correlations of a Two-Component Classical Plasma
NASA Astrophysics Data System (ADS)
Alastuey, Angel; Fantoni, Riccardo
2016-05-01
We consider an ionic fluid made with two species of mobile particles carrying either a positive or a negative charge. We derive a sum rule for the fourth moment of equilibrium charge correlations. Our method relies on the study of the system response to the potential created by a weak external charge distribution with slow spatial variations. The induced particle densities, and the resulting induced charge density, are then computed within density functional theory, where the free energy is expanded in powers of the density gradients. The comparison with the predictions of linear response theory provides a thermodynamical expression for the fourth moment of charge correlations, which involves the isothermal compressibility as well as suitably defined partial compressibilities. The familiar Stillinger-Lovett condition is also recovered as a by-product of our method, suggesting that the fourth moment sum rule should hold in any conducting phase. This is explicitly checked in the low density regime, within the Abe-Meeron diagrammatical expansions. Beyond its own interest, the fourth-moment sum rule should be useful for both analyzing and understanding recently observed behaviours near the ionic critical point.
Effective restoration of dipole sum rules within the renormalized random-phase approximation
NASA Astrophysics Data System (ADS)
Hung, N. Quang; Dang, N. Dinh; Hao, T. V. Nhan; Phuc, L. Tan
2016-12-01
The dipole excitations for calcium and zirconium isotopes are studied within the fully self-consistent Hartree-Fock mean field incorporated with the renormalized random-phase approximation (RRPA) using the Skyrme interaction SLy5. The RRPA takes into account the effect of ground-state correlations beyond RPA owing to the Pauli principle between the particle-hole pairs that form the RPA excitations as well as the correlations due to the particle-particle and hole-hole transitions, whose effects are treated here in an effective way. By comparing the RPA results with the RRPA ones, which are obtained for isoscalar (IS) and isovector (IV) dipole excitations in 48,52,58Ca and 90,96,110Zr, it is shown that ground-state correlations beyond the RPA reduce the IS transition strengths. They also shift up the energy of the lowest IV dipole state and slightly push down the peak energy of the IV giant dipole resonance. As the result, the energy-weighted sums of strengths of both IS and IV modes decrease, causing the violation of the corresponding energy-weighted sum rules (EWSR). It is shown that this sum rule violation can be eliminated by taking into account the contribution of the particle-particle and hole-hole excitations together with the particle-hole ones in a simple and perturbative way. Consequently, the ratio of the energy-weighted sum of strengths of the pygmy dipole resonance to that of the giant dipole resonance increases.
Perturbative corrections to Λ b → Λ form factors from QCD light-cone sum rules
NASA Astrophysics Data System (ADS)
Wang, Yu-Ming; Shen, Yue-Long
2016-02-01
We compute radiative corrections to Λ b → Λ from factors, at next-to-leading logarithmic accuracy, from QCD light-cone sum rules with Λ b -baryon distribution amplitudes. Employing the diagrammatic approach factorization of the vacuum-to-Λ b -baryon correlation function is justified at leading power in Λ /m b , with the aid of the method of regions. Hard functions entering the factorization formulae are identical to the corresponding matching coefficients of heavy-to-light currents from QCD onto soft-collinear effective theory. The universal jet function from integrating out the hard-collinear fluctuations exhibits richer structures compared with the one involved in the factorization expressions of the vacuum-to- B-meson correlation function. Based upon the QCD resummation improved sum rules we observe that the perturbative corrections at {O}({α}_s) shift the Λ b → Λ from factors at large recoil significantly and the dominant contribution originates from the next-to-leading order jet function instead of the hard coefficient functions. Having at hand the sum rule predictions for the Λ b → Λ from factors we further investigate several decay observables in the electro-weak penguin Λ b → Λ ℓ + ℓ - transitions in the factorization limit (i.e., ignoring the "non-factorizable" hadronic effects which cannot be expressed in terms of the Λ b → Λ from factors), including the invariant mass distribution of the lepton pair, the forward-backward asymmetry in the dilepton system and the longitudinal polarization fraction of the leptonic sector.
Tree level semileptonic {sigma}{sub b} to nucleon decay in light cone QCD sum rules
Azizi, K.; Ozpineci, A.; Bayar, M.; Sarac, Y.
2009-08-01
Using the most general form of the interpolating current of the heavy spin 1/2, {sigma}{sub b} baryon and distribution amplitudes of the nucleon, the transition form factors of the semileptonic {sigma}{sub b}{yields}Nl{nu} decay are calculated in the framework of light-cone QCD sum rules. It is obtained that the form factors satisfy the heavy quark effective theory relations. The obtained results for the related form factors are used to estimate the decay rate of this transition.
{kappa}K{sup +{pi}-} vertex in light cone QCD sum rules
Baytemir, G.; Sarac, Y.; Yilmaz, O.
2010-05-01
In this work we study the {kappa}K{sup +{pi}-} vertex in the framework of light cone QCD sum rules. We predict the coupling constant g{sub {kappa}K}{sup +}{sub {pi}}{sup -} to be g{sub {kappa}K}{sup +}{sub {pi}}{sup -}=(6.0{+-}1.0) GeV and estimate the scalar f{sub 0}-{sigma} mixing angle from the experimental ratio g{sup 2}({kappa}{yields}K{pi})/g{sup 2}({sigma}{yields}{pi}{pi}).
Finite-energy sum rules in eta photoproduction off a nucleon
Nys, Jannes; Mathieu, V.; Fernandez-Ramirez, Cesar; ...
2017-02-15
The reactionmore » $${\\gamma}N \\to {\\eta}N$$ is studied in the high-energy regime (with photon lab energies $$E_{\\gamma}^{\\textrm{lab}} > 4$$ GeV) using information from the resonance region through the use of finite-energy sum rules (FESR). We illustrate how analyticity allows one to map the t-dependence of the unknown Regge residue functions. As a result, we provide predictions for the energy dependence of the beam asymmetry at high energies.« less
B ---> pi and B ---> K transitions from QCD sum rules on the light cone
Ball, P.
1998-09-01
I calculate the form factors describing semileptonic and penguin-induced decays of B mesons into light pseudoscalar mesons. The form factors are calculated from QCD sum rules on the light-cone including contributions up to twist 4, radiative corrections to the leading twist contribution and SU(3)-breaking effects. The theoretical uncertainty is estimated to be \\sim 15%. The heavy-quark-limit relations between semileptonic and penguin form factors are found to be valid in the full accessible range of momentum transfer.
Flavor changing neutral current transition of B to a1 with light-cone sum rules
NASA Astrophysics Data System (ADS)
Momeni, S.; Khosravi, R.; Falahati, F.
2017-01-01
The B →a1ℓ+ℓ- decays occur by the electroweak penguin and box diagrams, which can be performed through the flavor changing neutral current (FCNC). We calculate the form factors of the FCNC B →a1 transitions in the light-cone sum rules approach, up to twist-4 distribution amplitudes of the axial vector meson a1. Forward-backward asymmetry, as well as branching ratios of B →a1ℓ+ℓ-, and B →a1γ decays are considered. A comparison is also made between our results and the predictions of other methods.
NASA Astrophysics Data System (ADS)
Huitu, Katri; Pandita, P. N.; Tiitola, Paavo
2015-10-01
We examine the deflected mirage mediation supersymmetry breaking (DMMSB) scenario, which combines three supersymmetry breaking scenarios, namely anomaly mediation, gravity mediation and gauge mediation using the one-loop renormalization group invariants (RGIs). We examine the effects on the RGIs at the threshold where the gauge messengers emerge, and derive the supersymmetry breaking parameters in terms of the RGIs. We further discuss whether the supersymmetry breaking mediation mechanism can be determined using a limited set of invariants, and derive sum rules valid for DMMSB below the gauge messenger scale. In addition we examine the implications of the measured Higgs mass for the DMMSB spectrum.
Stopping power of strongly coupled electronic plasmas: sum rules and asymptotic forms.
Ortner, J; Tkachenko, I M
2001-02-01
The stopping power of coupled electronic plasmas is investigated. Within the dielectric formalism and employing the method of frequency moments for the dielectric function we obtain a general formula describing the linear stopping power of a coupled plasma. Analytical results for the low- and high-projectile-velocity asymptotic forms are obtained. A sum rule for the plasma heavy ions linear stopping power projectile velocity distribution is established to be related to the dielectric permeability "negative" frequency moment. This permits for a simple interpretation of stopping power data.
Generalized heavy-to-light form factors in light-cone sum rules
NASA Astrophysics Data System (ADS)
Meißner, Ulf-G.; Wang, Wei
2014-03-01
We study the form factors for a heavy meson into the S-wave Kπ/ππ system with an invariant mass below 1 GeV. The mesonic final state interactions are described in terms of the scalar form factors, which are obtained from unitarized chiral perturbation theory. Employing generalized light-cone distribution amplitudes, we compute the heavy-to-light transition using light-cone sum rules. Our approach simultaneously respects constraints from analyticity and unitarity, and also takes advantage of the power expansion in the 1/mb and the strong coupling constant.
Power corrections to the Bjoerken and the Gross--Llewellyn Smith sum rules in QCD
Braun, V.M.; Kolesnichenko, A.V.
1987-04-01
In the framework of QCD sum rules we calculate the power corrections proportional to 1/Q/sup 2/ (twist 4) to the first moment of the structure functions of deep inelastic ..nu..p scattering. In contrast to previous estimates they turn out to be not small, of the order of the leading scaling-violating correction in perturbation theory at Q/sup 2/--1 GeV/sup 2/ and of the same sign. We discuss possible higher-twist contributions.
{sup 3}He Spin-Dependent Cross Sections and Sum Rules
Slifer, K.; Auerbach, L.; Choi, Seonho; Incerti, S.; Lakuriqi, E.; Meziani, Z.-E.; Amarian, M.; Ketikyan, A.; Voskanian, H.; Averett, T.; Berthot, J.; Bertin, P.; DiSalvo, R.; Fonvieille, H.; Laveissiere, G.; Roblin, Y.
2008-07-11
We present a measurement of the spin-dependent cross sections for the {sup 3}He-vector (e-vector,e{sup '})X reaction in the quasielastic and resonance regions at a four-momentum transfer 0.1{<=}Q{sup 2}{<=}0.9 GeV{sup 2}. The spin-structure functions have been extracted and used to evaluate the nuclear Burkhardt-Cottingham and extended Gerasimov-Drell-Hearn sum rules for the first time. The data are also compared to an impulse approximation calculation and an exact three-body Faddeev calculation in the quasielastic region.
Magnetic moment for the negative parity Λ → Σ0 transition in light cone QCD sum rules
NASA Astrophysics Data System (ADS)
Aliev, T. M.; Savcı, M.
2016-07-01
The magnetic moment of the Λ →Σ0 transition between negative parity baryons is calculated in framework of the QCD sum rules approach by using the general form of the interpolating currents. The pollution arising from the positive-to-positive, and positive-to-negative parity baryons is eliminated by constructing the sum rules for different Lorentz structures. A comparison of our result with the predictions of the results of other approaches for the positive parity baryons is presented.
NASA Astrophysics Data System (ADS)
Kumar, Ashok; Thakkar, Ajit J.
2011-11-01
Experimental photoabsorption cross-sections combined with constraints provided by the Kuhn-Reiche-Thomas sum rule and the high-energy behavior of the dipole-oscillator-strength density are used to construct dipole oscillator strength distributions for buckminsterfullerene (C60). The distributions are used to predict dipole sum rules Sk, mean excitation energies Ik, the frequency dependent polarizability, and C6 coefficients for the long-range dipole-dipole interactions of C60 with a variety of atoms and molecules.
Ball, Patricia; Braun, Vladimir M.
1997-01-01
The existing calculations of the form factors describing the decay B→ρeν from QCD sum rules have yielded conflicting results at small values of the invariant mass squared of the lepton pair. We demonstrate that the disagreement originates from the failure of the short-distance expansion to describe the ρ meson distribution amplitude in the region where almost the whole momentum is carried by one of the constituents. This limits the applicability of QCD sum rules based on the short-distance expansion of a three-point correlation function to heavy-to-light transitions and calls for an expansion around the light cone, as realized in the light-cone sum rule approach. We derive and update light-cone sum rules for all the semileptonic form factors, using recent results on the ρ meson distribution amplitudes. The results are presented in detail together with a careful analysis of the uncertainties, including estimates of higher-twist effects, and compared to lattice calculations and recent CLEO measurements. We also derive a set of “improved” three-point sum rules, in which some of the problems of the short-distance expansion are avoided and whose results agree to good accuracy with those from light-cone sum rules.
Heavy-light diquark masses from QCD sum rules and constituent diquark models of tetraquarks
NASA Astrophysics Data System (ADS)
Kleiv, R. T.; Steele, T. G.; Zhang, Ailin; Blokland, Ian
2013-06-01
Diquarks with JP=0±, 1± containing a heavy (charm or bottom) quark and a light quark are investigated using QCD Laplace sum rules. Masses are determined using appropriately constructed gauge invariant correlation functions, including for the first time next-to-leading order perturbative contributions. The JP=0+ and 1+ charm-light diquark masses are, respectively, found to be 1.86±0.05 and 1.87±0.10GeV, while those of the 0+ and 1+ bottom-light diquarks are both determined to be 5.08±0.04GeV. The sum rules derived for heavy-light diquarks with negative parity are poorly behaved and do not permit unambiguous mass predictions, in agreement with previous results for negative parity light diquarks. The scalar and axial vector heavy-light diquark masses are degenerate within uncertainty, as expected by heavy quark symmetry considerations. Furthermore, these mass predictions are in good agreement with masses extracted in constituent diquark models of the tetraquark candidates X(3872) and Yb(10890). Thus these results provide QCD support for the interpretation of the X(3872) and Yb(10890) as JPC=1++ tetraquark states composed of diquark clusters. Further implications for tetraquarks among the heavy quarkoniumlike XYZ states are discussed.
Measurement of the Neutron Spin Structure Function and Its Implications for QCD Sum Rules
Xu, J
2004-01-06
The authors have determined the neutron spin structure function g{sub 1}{sup n} over the range 0.03 {le} x {le} 0.6 at an average Q{sup 2} of 2(GeV/c){sup 2} by measuring the asymmetry in deep inelastic scattering of polarized electrons from a polarized {sup 3}He target. The experiment was performed at SLAC and used energies between 19 and 26 GeV. The neutron asymmetry turned out to be small and negative, and the integral of the neutron spin structure function is {integral}{sub 0}{sup 1}g{sub 1}{sup n}(x)dx = -0.024 {+-} 0.006(stat.) {+-} 0.008(syst.). Combined with the current available worldwide proton data, this result confirmed the Bjorken sum rule at 10% level, once high-order perturbative QCD corrections are taken into account. The Ellis-Jaffe sum rule for the neutron predicts {integral}{sub 0}{sup 1} g{sub 1}{sup n}(x)dx = -0.010 {+-} 0.012, roughly consistent with their result.
Reanalysis of the X(3915) , X(4500) and X(4700) with QCD sum rules
NASA Astrophysics Data System (ADS)
Wang, Zhi-Gang
2017-02-01
In this article, we study the Cγ_5⊗ γ_5C type and C⊗ C type scalar csbar{c}bar{s} tetraquark states with the QCD sum rules by calculating the contributions of the vacuum condensates up to dimension 10 in a consistent way. The ground state masses M_{Cγ_5⊗ γ_5C}=3.89± 0.05 GeV and M_{C⊗ C} =5.48±0.10 GeV support assigning the X(3915) as the ground state Cγ_5⊗ γ_5C type tetraquark state with J^{PC}=0^{++} , but do not support assigning the X(4700) as the ground state C⊗ C type csbar{c}bar{s} tetraquark state with J^{PC}=0^{++} . Then we tentatively assign the X(3915) and X(4500) as the 1 S and 2 S Cγ_5⊗ γ_5C type scalar csbar{c}bar{s} tetraquark states respectively, and obtain the 1 S mass M_{1S}= 3.85^{+0.18}_{-0.17} GeV and 2 S mass M 2S = 4.35+0.10 -0.11 GeV from the QCD sum rules, which support assigning the X(3915) as the 1 S Cγ_5⊗ γ_5C type tetraquark state, but do not support assigning the X(4500) as the 2 S Cγ_5⊗ γ_5C type tetraquark state.
Viscosity of strongly interacting quantum fluids: Spectral functions and sum rules
Taylor, Edward; Randeria, Mohit
2010-05-15
The viscosity of strongly interacting systems is a topic of great interest in diverse fields. We focus here on the bulk and shear viscosities of nonrelativistic quantum fluids, with particular emphasis on strongly interacting ultracold Fermi gases. We use Kubo formulas for the bulk and shear viscosity spectral functions, {zeta}({omega}) and {eta}({omega}), respectively, to derive exact, nonperturbative results. Our results include a microscopic connection between the shear viscosity {eta} and the normal-fluid density {rho}{sub n}; sum rules for {zeta}({omega}) and {eta}({omega}) and their evolution through the BCS-BEC crossover (where BEC denotes Bose-Einstein condensate); and universal high-frequency tails for {eta}({omega}) and the dynamic structure factor S(q,{omega}). We use our sum rules to show that, at unitarity, {zeta}({omega}) is identically zero and thus relate {eta}({omega}) to density-density correlations. We predict that frequency-dependent shear viscosity {eta}({omega}) of the unitary Fermi gas can be experimentally measured using Bragg spectroscopy.
Spectral sum rules and magneto-roton as emergent graviton in fractional quantum Hall effect
Golkar, Siavash; Nguyen, Dung X.; Son, Dam T.
2016-01-05
Here, we consider gapped fractional quantum Hall states on the lowest Landau level when the Coulomb energy is much smaller than the cyclotron energy. We introduce two spectral densities, ρ_{T}(ω) and $\\bar{p}$_{T}(ω), which are proportional to the probabilities of absorption of circularly polarized gravitons by the quantum Hall system. We prove three sum rules relating these spectral densities with the shift S, the q^{4} coefficient of the static structure factor S_{4}, and the high-frequency shear modulus of the ground state μ_{∞}, which is precisely defined. We confirm an inequality, first suggested by Haldane, that S_{4} is bounded from below by |S–1|/8. The Laughlin wavefunction saturates this bound, which we argue to imply that systems with ground state wavefunctions close to Laughlin’s absorb gravitons of predominantly one circular polarization. We consider a nonlinear model where the sum rules are saturated by a single magneto-roton mode. In this model, the magneto-roton arises from the mixing between oscillations of an internal metric and the hydrodynamic motion. Implications for experiments are briefly discussed.
Spectral sum rules and magneto-roton as emergent graviton in fractional quantum Hall effect
Golkar, Siavash; Nguyen, Dung X.; Son, Dam T.
2016-01-05
Here, we consider gapped fractional quantum Hall states on the lowest Landau level when the Coulomb energy is much smaller than the cyclotron energy. We introduce two spectral densities, ρT(ω) andmore » $$\\bar{p}$$T(ω), which are proportional to the probabilities of absorption of circularly polarized gravitons by the quantum Hall system. We prove three sum rules relating these spectral densities with the shift S, the q4 coefficient of the static structure factor S4, and the high-frequency shear modulus of the ground state μ∞, which is precisely defined. We confirm an inequality, first suggested by Haldane, that S4 is bounded from below by |S–1|/8. The Laughlin wavefunction saturates this bound, which we argue to imply that systems with ground state wavefunctions close to Laughlin’s absorb gravitons of predominantly one circular polarization. We consider a nonlinear model where the sum rules are saturated by a single magneto-roton mode. In this model, the magneto-roton arises from the mixing between oscillations of an internal metric and the hydrodynamic motion. Implications for experiments are briefly discussed.« less
Near critical electrolytes: Are the charge-charge sum rules obeyed?
NASA Astrophysics Data System (ADS)
Das, Subir K.; Kim, Young C.; Fisher, Michael E.
2012-08-01
In an electrolyte solution the charge-charge structure factor obeys S_{ZZ}(k;T,ρ )=0+ξ _{Z,1}^2k^2-ξ _{Z,2}^4k^4+\\cdots, where ξZ, 1 and ξZ, 2 are the second- and fourth-moment charge-charge correlation lengths depending on the temperature T and the overall ion density ρ. The vanishing of the leading term, the first Stillinger-Lovett (SL) sum rule, simply reflects bulk electroneutrality. The second SL rule, or second-moment condition, dictates that ξZ, 1 = ξD, where the Debye screening length ξD is proportional to √{T/ρ }. In this paper we present results from grand canonical Monte Carlo simulations of a fully size and charge symmetric 1:1 (finely-discretized) hard-sphere electrolyte, or restricted primitive model. By design, electroneutrality is imposed during the simulations, so satisfying the first sum rule automatically. However, careful finite-size scaling analyses of extensive histogram reweighted data indicate that the second-moment condition is violated at criticality, ξ _{Z,1}^c exceeding ξ _D^c by approximately 8%. It is also found that ξ _{Z,2}^4 diverges to +∞ as T → Tc in a manner closely mirroring the density-density fluctuations, SNN(0). These findings contradict generalized Debye-Hückel theory and also the exactly soluble charge-symmetric spherical models, both of which support the second-moment condition at criticality and the finiteness of the fourth-moment. Nevertheless, the observed behavior is strikingly similar to that of the charge-asymmetric spherical models.
Annuity and lump-sum decisions in defined benefit plans: the role of plan rules.
Banerjee, Sudipto
2013-01-01
Amidst growing concerns about workers outliving their retirement savings, a key question-both as a matter of national retirement policy and understanding the potential role of plan design and education in influencing individual decision-making-is how many retiring workers actually choose to annuitize (to take a stream of lifetime income) vs. opting for a lump-sum payment. The key finding of this study is that differences in defined benefit (DB) plan rules or features result in very different annuitization rates in DB plans. In fact, the results show that the rate of annuitization varies directly with the degree to which plan rules restrict the ability to choose a partial or lump-sum distribution. This study shows that annuitization rates vary significantly across these different plan types, which makes any attempt to combine the annuitization rates across these different plan types uninformative. Combining all the plans across the years 2005-2010, workers who made their payout decision between ages 50 and 75 had a minimum job tenure of five years, a minimum account balance of $5,000, and had an annuitization rate of 65.8 percent. But within this group of workers, those who had no plan restrictions on a lump-sum distribution had an annuitization rate of only 27.3 percent. In all the years studied, plans with no lump-sum distribution (LSD) options have the highest annuitization rates, very close to 100 percent. Traditional defined benefit and cash balance plans with no restrictionson LSDs had the lowest annuitization rates. In 2010, the annuitization rate for all plans combined was 65.5 percent, while for plans with no LSD option it was 98.8 percent, but the annuitization rate for defined benefit plans with no restrictions on LSDs was 44.3 percent, while for cash balance plans with no restrictions on LSDs it was 22.3 percent. For older workers across most plan types, annuitization rates increase steadily with account balance, but this is not the case for younger
The inclusive flavor-breaking τ-based sum rule determination of Vus
NASA Astrophysics Data System (ADS)
Maltman, K.; Hudspith, R. J.; Izubuchi, T.; Lewis, R.; Ohki, H.; Zanotti, J. M.
2017-06-01
We revisit the puzzle of the > 3 σ low (c.f. three-family-unitarity expections) determination of Vus from the conventional implementation of flavor-breaking (FB) finite-energy sum rules (FESRs) employing inclusive hadronic τ decay data. Problems with this implementation are identified and an alternative implementation which cures them described. Using this new implementation and preliminary BaBar results for the exclusive τ →K-π0ντ find Vus = 0.2228(23)exp(6)th, in excellent agreement with results from other sources. Limitations on the near-term possibilities for reducing experimental errors in this approach are highlighted, and a new proposal for improving this situation via dispersive analyses of strange hadronic τ data using lattice data as input described.
Mass tensor in the Bohr Hamiltonian from the nondiagonal energy weighted sum rules
Jolos, R. V.; Brentano, P. von
2009-04-15
Relations are derived in the framework of the Bohr Hamiltonian that express the matrix elements of the deformation-dependent components of the mass tensor through the experimental data on the energies and the E2 transitions relating the low-lying collective states. These relations extend the previously obtained results for the intrinsic mass coefficients of the well-deformed axially symmetric nuclei on nuclei of arbitrary shape. The expression for the mass tensor is suggested, which is sufficient to satisfy the existing experimental data on the energy weighted sum rules for the E2 transitions for the low-lying collective quadrupole excitations. The mass tensor is determined for {sup 106,108}Pd, {sup 108-112}Cd, {sup 134}Ba, {sup 150}Nd, {sup 150-154}Sm, {sup 154-160}Gd, {sup 164}Dy, {sup 172}Yb, {sup 178}Hf, {sup 188-192}Os, and {sup 194-196}Pt.
Analysis of the QQ\\bar{Q}\\bar{Q} tetraquark states with QCD sum rules
NASA Astrophysics Data System (ADS)
Wang, Zhi-Gang
2017-07-01
In this article, we study the J^{PC}=0^{++} and 2^{++} QQ\\bar{Q}\\bar{Q} tetraquark states with the QCD sum rules, and we obtain the predictions M_{X(cc\\bar{c}\\bar{c},0^{++})} =5.99± 0.08 GeV, M_{X(cc\\bar{c}\\bar{c},2^{++})} =6.09± 0.08 GeV, M_{X(bb\\bar{b}\\bar{b},0^{++})} =18.84± 0.09 GeV and M_{X(bb\\bar{b}\\bar{b},2^{++})} =18.85± 0.09 GeV, which can be confronted to the experimental data in the future. Furthermore, we illustrate that the diquark-antidiquark type tetraquark state can be taken as a special superposition of a series of meson-meson pairs and that it embodies the net effects.
Masses of Open-Flavour Heavy-Light Hybrids from QCD Sum Rules
NASA Astrophysics Data System (ADS)
Ho, Jason; Harnett, Derek; Steele, Tom
2017-01-01
Our current understanding of the strong interaction (QCD) permits the construction of colour singlet states with novel structures that do not fit within the traditional quark model, including hybrid mesons. To date, though other exotic structures such as pentaquark and tetraquark states have been confirmed, no unambiguous hybrid meson signals have been observed. However, with data collection at the GlueX experiment ongoing and with the construction of the PANDA experiment at FAIR, the opportunity to observe hybrid states has never been better. As theoretical calculations are a necessary piece for the identification of any observed experimental resonance, we present our mass predictions of heavy-light open-flavour hybrid mesons using QCD Laplace sum-rules for all scalar and vector JP channels, and including non-perturbative condensate contributions up to six-dimensions.
Sum-rule corrections: A route to error cancellations in correlation matrix renormalisation theory
Liu, C.; Liu, J.; Yao, Y. X.; ...
2017-01-16
Here, we recently proposed the correlation matrix renormalisation (CMR) theory to efficiently and accurately calculate ground state total energy of molecular systems, based on the Gutzwiller variational wavefunction (GWF) to treat the electronic correlation effects. To help reduce numerical complications and better adapt the CMR to infinite lattice systems, we need to further refine the way to minimise the error originated from the approximations in the theory. This conference proceeding reports our recent progress on this key issue, namely, we obtained a simple analytical functional form for the one-electron renormalisation factors, and introduced a novel sum-rule correction for a moremore » accurate description of the intersite electron correlations. Benchmark calculations are performed on a set of molecules to show the reasonable accuracy of the method.« less
Malila, Jussi; McGraw, Robert; Laaksonen, Ari; ...
2015-01-07
Despite recent advances in monitoring nucleation from a vapor at close-to-molecular resolution, the identity of the critical cluster, forming the bottleneck for the nucleation process, remains elusive. During past twenty years, the first nucleation theorem has been often used to extract the size of the critical cluster from nucleation rate measurements. However, derivations of the first nucleation theorem invoke certain questionable assumptions that may fail, e.g., in the case of atmospheric new particle formation, including absence of subcritical cluster losses and heterogeneous nucleation on pre-existing nanoparticles. Here we extend the kinetic derivation of the first nucleation theorem to give amore » general framework to include such processes, yielding sum rules connecting the size dependent particle formation and loss rates to the corresponding loss-free nucleation rate and the apparent critical size from a naïve application of the first nucleation theorem that neglects them.« less
Sum rules and spectral density flow in QCD and in superconformal theories
NASA Astrophysics Data System (ADS)
Costantini, Antonio; Delle Rose, Luigi; Serino, Mirko
2014-11-01
We discuss the signature of the anomalous breaking of the superconformal symmetry in N = 1 super Yang Mills theory and its manifestation in the form of anomaly poles. Moreover, we describe the massive deformations of the N = 1 theory and the spectral densities of the corresponding anomaly form factors. These are characterized by spectral densities which flow with the mass deformation and turn the continuum contributions from the two-particle cuts of the intermediate states into poles, with a single sum rule satisfied by each component. The poles can be interpreted as signaling the exchange of a composite axion/dilaton/dilatino (ADD) multiplet in the effective Lagrangian. We conclude that global anomalous currents characterized by a single flow in the perturbative picture always predict the existence of composite interpolating fields.
Understanding close-lying exotic charmonia states within QCD sum rules
NASA Astrophysics Data System (ADS)
Martínez Torres, A.; Khemchandani, K. P.; Dias, J. M.; Navarra, F. S.; Nielsen, M.
2017-10-01
Motivated by the experimental findings of some new exotic states decaying into channels like J / ψϕ, we investigate the formation of resonances/bound states in the Ds* Dbars* system using QCD sum rules. To do this we start with a current of the type vector times vector and use spin projectors to separate the spin 0, 1 and 2 contributions to the correlation function. We find three states with isospin 0, nearly spin degenerate, with a mass around 4.1 GeV. We have also investigated the decay of these states to J / ψϕ and provide the corresponding partial widths. Such information should be useful for experimental studies in future.
Pinched weights and duality violation in QCD sum rules: A critical analysis
Gonzalez-Alonso, Martin; Pich, Antonio; Prades, Joaquim
2010-07-01
We analyze the so-called pinched weights, that are generally thought to reduce the violation of quark-hadron duality in finite-energy sum rules. After showing how this is not true in general, we explain how to address this question for the left-right correlator and any particular pinched weight, taking advantage of our previous work [1], where the possible high-energy behavior of the left-right spectral function was studied. In particular, we show that the use of pinched weights allows to determine with high accuracy the dimension six and eight contributions in the operator-product expansion, O{sub 6}=(-4.3{sub -0.7}{sup +0.9})x10{sup -3} GeV{sup 6} and O{sub 8}=(-7.2{sub -5.3}{sup +4.2})x10{sup -3} GeV{sup 8}.
Sum-Rule Constraints on the Surface State Conductance of Topological Insulators
NASA Astrophysics Data System (ADS)
Post, K. W.; Chapler, B. C.; Liu, M. K.; Wu, J. S.; Stinson, H. T.; Goldflam, M. D.; Richardella, A. R.; Lee, J. S.; Reijnders, A. A.; Burch, K. S.; Fogler, M. M.; Samarth, N.; Basov, D. N.
2015-09-01
We report the Drude oscillator strength D and the magnitude of the bulk band gap Eg of the epitaxially grown, topological insulator (Bi ,Sb )2Te3 . The magnitude of Eg, in conjunction with the model independent f -sum rule, allows us to establish an upper bound for the magnitude of D expected in a typical Dirac-like system composed of linear bands. The experimentally observed D is found to be at or below this theoretical upper bound, demonstrating the effectiveness of alloying in eliminating bulk charge carriers. Moreover, direct comparison of the measured D to magnetoresistance measurements of the same sample supports assignment of the observed low-energy conduction to topological surface states.
New sum rule determination of the nucleon mass and strangeness content
NASA Astrophysics Data System (ADS)
Nasrallah, N. F.; Schilcher, K.
2014-04-01
A new QCD calculation of the mass of the nucleon is presented. It makes use of a polynomial kernel in the dispersion integrals tailored to practically eliminate the contribution of the unknown 1/2+ and 1/2- continuum. This approach avoids the arbitrariness and instability attached to the Borel kernel used in previous sum rules calculations. Our method yields stable results for the nucleon mass and coupling for standard values of the condensates. The prediction of the nucleon mass in the chiral limit is mN=(830±50) MeV. When the nucleon sigma terms are added this gives MN=990±50 MeV, which leaves little room for a large strangeness content of the nucleon.
Study of the D*ρ system using QCD sum rules
Torres, A. Martínez; Khemchandani, K. P.; Nielsen, M.; Navarra, F. S.; Oset, E.
2014-11-11
In this proceeding we present a study of the D*ρ system made by using the method of QCD sum rules. Considering isospin and spin projectors, we investigate the different configurations and obtain three D* mesons with isospin I = 1/2, spin S = 0, 1, 2 and with masses 2500±67 MeV, 2523±60 MeV, and 2439±119 MeV, respectively. The last state can be related to D{sub 2}{sup *} (2460) (spin 2) listed by the Particle Data Group, while one of the first two might be associated with D*(2640), whose spin-parity is unknown. In the case of I = 3/2 we also find evidences of three states with spin 0, 1 and 2, respectively, with masses 2467±82 MeV, 2420±128 MeV, and 2550±56 MeV.
Sum rules for generalized electron-pair moments of Hartree-Fock orbitals
NASA Astrophysics Data System (ADS)
Koga, Toshikatsu
2001-05-01
For many-electron systems, the generalized electron-pair density function g(q;a,b) represents the probability density function for the magnitude |ari+brj| of two-electron vector ari+brj to be q, where a and b are real-valued parameters. For Hartree-Fock wave functions, decomposition of g(q;a,b) into spin-orbital-pair components gij(q;a,b) shows that the second moments
SCET Sum Rules for B to P and B to V Transition Form Factors
De Fazio, Fulvia; Feldmann, Thorsten; Hurth, Tobias; /CERN /SLAC
2007-12-18
We investigate sum rules for heavy-to-light transition form factors at large recoil derived from correlation functions with interpolating currents for light pseudoscalar or vector fields in soft-collinear effective theory (SCET). We consider both, factorizable and nonfactorizable contributions at leading power in the {Lambda}/m{sub b} expansion and to first order in the strong coupling constant {alpha}{sub s}, neglecting contributions from 3-particle distribution amplitudes in the B-meson. We pay particular attention to various sources of parametric and systematic uncertainties. We also discuss certain form factor ratios where part of the hadronic uncertainties related to the B-meson distribution amplitude and to logarithmically enhanced {alpha}{sub s} corrections cancel.
Molecular orbital study of the bond-valence sum rule using Lewis-electron pair theory.
Mohri, Fumihito
2003-04-01
The bond-valence sum rule has been examined by molecular-orbital methods related to spin-coupling matrix theory [Okada & Fueno (1976). Bull. Chem. Soc. Jpn, 49, 1524-1530], to give a new formulation of the Lewis-electron pair concept. It is shown that the 'pair-coupling population' between atoms M and X exhibits the same behaviour as the bond valence between them. A quantum chemical definition for bond valence is proposed and successfully applied to Al(2)Cl(6), Te(4)Cl(16) and Al(2)Be(3)(SiO(3))(6) (beryl). Using an alternative bond-valence definition it is shown that for oxides the bond valence can possibly be taken as the double pair-coupling population.
Analysis of the strong coupling constant and the decay width of with QCD sum rules
NASA Astrophysics Data System (ADS)
Yu, Guo-Liang; Li, Zhen-Yu; Wang, Zhi-Gang
2015-06-01
In this article, we calculate the form factors and the coupling constant of the vertex using the three-point QCD sum rules. We consider the contributions of the vacuum condensates up to dimension 7 in the operator product expansion. And all possible off-shell cases are considered, , and , resulting in three different form factors. Then we fit the form factors into analytical functions and extrapolate them into time-like regions, which giving the coupling constant for the process. Our analysis indicates that the coupling constant for this vertex is . The results of this work are very useful in the other phenomenological analysis. As an application, we calculate the coupling constant for the decay channel and analyze the width of this decay with the assumption of the vector meson dominance of the intermediate . Our final result about the decay width of this decay channel is.
Sum-rule constraints on the surface state conductance of topological insulators.
Post, K W; Chapler, B C; Liu, M K; Wu, J S; Stinson, H T; Goldflam, M D; Richardella, A R; Lee, J S; Reijnders, A A; Burch, K S; Fogler, M M; Samarth, N; Basov, D N
2015-09-11
We report the Drude oscillator strength D and the magnitude of the bulk band gap E_{g} of the epitaxially grown, topological insulator (Bi,Sb)_{2}Te_{3}. The magnitude of E_{g}, in conjunction with the model independent f-sum rule, allows us to establish an upper bound for the magnitude of D expected in a typical Dirac-like system composed of linear bands. The experimentally observed D is found to be at or below this theoretical upper bound, demonstrating the effectiveness of alloying in eliminating bulk charge carriers. Moreover, direct comparison of the measured D to magnetoresistance measurements of the same sample supports assignment of the observed low-energy conduction to topological surface states.
Liu, C; Liu, J; Yao, Y X; Wu, P; Wang, C Z; Ho, K M
2016-10-11
We recently proposed the correlation matrix renormalization (CMR) theory to treat the electronic correlation effects [Phys. Rev. B 2014, 89, 045131 and Sci. Rep. 2015, 5, 13478] in ground state total energy calculations of molecular systems using the Gutzwiller variational wave function (GWF). By adopting a number of approximations, the computational effort of the CMR can be reduced to a level similar to Hartree-Fock calculations. This paper reports our recent progress in minimizing the error originating from some of these approximations. We introduce a novel sum-rule correction to obtain a more accurate description of the intersite electron correlation effects in total energy calculations. Benchmark calculations are performed on a set of molecules to show the reasonable accuracy of the method.
NASA Astrophysics Data System (ADS)
Cabrera-Trujillo, R.
2017-08-01
Sum rule relations over the excitation spectrum of a quantum system contain information about both the energy spectrum and eigenfunctions of the system in a compact form, particularly regarding closure relations. In this work, the effects of pressure induced by a spherical cavity on an atomic hydrogen impurity on the dipole oscillator strength (DOS) sum rule, S k , and its logarithmic version, L k , are studied by means of a numerical approach based on a finite-difference solution to the Schrödinger equation. Pressure effects are accounted for by means of a spherical cavity of radius R 0 immersed in a medium characterized by a penetrable potential height V 0. The DOS sum rules S k and L k are investigated as a function of these cavity parameters and thus directly related to the impurity static pressure and surrounding material. One finds that the sum rules are fulfilled within the numerical precision for low pressure conditions. However, when the barrier height is large or infinite (a non-penetrable cavity), the sum rule, for positive k, differs from its closure relation. One finds that this occurs for a cavity radius {R}0< 6 au, corresponding to a pressure such that the first p-state that contributes to the sum rule has positive energy and it is due to the fact that the spherical confinement cavity potential dominates over the Coulombic interaction for the hydrogenic impurity. Thus, as pressure increases, the excitation spectrum approaches that of a particle confined by a spherical cavity while the ground state is slightly affected by the cavity and more closely resembles a hydrogenic atom. Therefore, the sum rule over the excitation spectrum tends to a particle confined by a spherical cavity, while the closure relation gives that of a confined hydrogen atom in the ground state. For negative k, low excitations are the most important and this behavior is not presented. As the {S}-2 sum rule is the static dipole polarizability, the results are compared to available
Isospin breaking in the decay constants of heavy mesons from QCD sum rules
NASA Astrophysics Data System (ADS)
Lucha, Wolfgang; Melikhov, Dmitri; Simula, Silvano
2017-02-01
We present a study of the strong isospin-breaking (IB) effect, due in QCD to the difference between u- and d-quark masses, in the leptonic decay constants of charmed and beauty pseudoscalar and vector mesons using the method of QCD sum rules. We apply the sum-rule analysis to the decay constants of mesons containing one heavy quark and one light quark with the light mass in the range from the average u / d quark mass to the strange-quark mass. We then analyse the dependence of the decay constants on the light-quark mass and extract with good accuracy the IB ratios of decay constants at leading order in the mass difference (md -mu), obtaining: (fD+ -fD0) /fD = 0.0047 (6), (fD*+ -fD*0) /fD* = 0.0068 (9), (fB0 -fB+) /fB = 0.0047 (6), and (fB*0 -fB*+) /fB* = 0.0045 (5), which yield: fD+ -fD0 = 0.97 ± 0.13 MeV, fD*+ -fD*0 = 1.73 ± 0.27 MeV, fB0 -fB+ = 0.90 ± 0.13 MeV, fB*0 -fB*+ = 0.81 ± 0.11 MeV. In the case of the D-meson our finding is consistent with recent lattice QCD results, whereas it is much lower in the case of the B-meson showing a tension of ≈3 standard deviations.
NASA Astrophysics Data System (ADS)
Rodríguez-Núñez, J. J.; Ţifrea, I.; Magalhães, S. G.
2000-08-01
Restudying the non-Fermi-liquid one-particle Green functions (NFLGF) we have extended the work of Balatsky [Philos. Mag. Lett. 68, 251 (1993)] and Yin and Chakravarty [Int. J. Mod. Phys. B 10, 805 (1996)], among others. We use the moment approach of Nolting [Z. Phys. 255, 25 (1972)] to compute the unknown parameters of the NFLGF's in the framework of the Hubbard model. The zeroth-order moment requires that our one-particle Green functions describe fermionic degrees of freedom. In order to satisfy the first-order sum rule, a renormalization, γ≠1, of the free-electron mass is called for. The second-order sum rule or moment imposes a relation between the non-Fermi-liquid parameter, α, the Coulomb interaction, U, and the frequency cutoff, ωc. We have calculated the effect of the mass renormalization factor, γ, on some physical quantities, such as (i) the correlated momentum distribution function, nc(k-->), close to the effective chemical potential, at T=0; (ii) the superconducting critical temperature, Tc; and (iii) the superconducting critical interaction, λcr, and compared them with analytical results found in the literature. Also, we have calculated the isotope effect, α', for non-Fermi-liquid systems, which reduces to α'=1/2 (the BCS result) when α-->0. As a case of non-Fermi-liquid systems, in the Appendix, we have studied two inequivalent coupled Hubbard layers for which we calculate the one-particle spectral functions on the layers and perpendicular to them. We discuss the features which appear due to the shift in the two effective chemical potentials and propose some experiments to detect the features found from our expressions.
QCD sum rule calculation of quark-gluon three-body components in the B-meson wave function
Nishikawa, Tetsuo; Tanaka, Kazuhiro
2011-10-21
We discuss the QCD sum rule calculation of the heavy-quark effective theory parameters {lambda}{sub E} and {lambda}{sub H}, which represent quark-gluon three-body components in the B-meson wave function. We update the sum rules for {lambda}{sub E,H} calculating the new higher-order contributions to the operator product expansion for the corresponding correlator, i.e., the order {alpha}{sub s} radiative corrections to the Wilson coefficients associated with the dimension-5 quark-gluon mixed condensate, and the power corrections due to the dimension-6 vacuum condensates. We find that the new radiative corrections significantly improve stability of the corresponding Borel sum rules, modifying the values of {lambda}{sub E,H}.
Yan, Xin -Hu; Ye, Yun -Xiu; Chen, Jian -Ping; ...
2015-07-17
The radiation and ionization energy loss are presented for single arm Monte Carlo simulation for the GDH sum rule experiment in Hall-A at Jefferson Lab. Radiation and ionization energy loss are discussed formore » $$^{12}C$$ elastic scattering simulation. The relative momentum ratio $$\\frac{\\Delta p}{p}$$ and $$^{12}C$$ elastic cross section are compared without and with radiation energy loss and a reasonable shape is obtained by the simulation. The total energy loss distribution is obtained, showing a Landau shape for $$^{12}C$$ elastic scattering. This simulation work will give good support for radiation correction analysis of the GDH sum rule experiment.« less
Yan, Xin -Hu; Ye, Yun -Xiu; Chen, Jian -Ping; Lu, Hai -Jiang; Zhu, Peng -Jia; Jiang, Feng -Jian
2015-07-17
The radiation and ionization energy loss are presented for single arm Monte Carlo simulation for the GDH sum rule experiment in Hall-A at Jefferson Lab. Radiation and ionization energy loss are discussed for $^{12}C$ elastic scattering simulation. The relative momentum ratio $\\frac{\\Delta p}{p}$ and $^{12}C$ elastic cross section are compared without and with radiation energy loss and a reasonable shape is obtained by the simulation. The total energy loss distribution is obtained, showing a Landau shape for $^{12}C$ elastic scattering. This simulation work will give good support for radiation correction analysis of the GDH sum rule experiment.
NASA Astrophysics Data System (ADS)
Kumar, Ashok; Thakkar, Ajit J.
2017-03-01
Dipole oscillator strength distributions for Br2 and BrCN are constructed from photoabsorption cross-sections combined with constraints provided by the Kuhn-Reiche-Thomas sum rule, the high-energy behavior of the dipole-oscillator-strength density and molar refractivity data when available. The distributions are used to predict dipole sum rules S (k) , mean excitation energies I (k) , and van der Waals C6 coefficients. Coupled-cluster calculations of the static dipole polarizabilities of Br2 and BrCN are reported for comparison with the values of S (- 2) extracted from the distributions.
Data on the Gross--Llewellyn Smith sum rule as a function of q/sup 2/
Bolognese, T.; Fritze, P.; Morfin, J.; Perkins, D.H.; Powell, K.; Scott, W.G.
1983-01-24
Data are presented on the Gross--Llewellyn Smith sum rule obtained from combined narrow-band neon and Freon bubble-chamber neutrino-antineutrino experiments. Remarkably no significant deviation from the parton-model prediction for the sum rule is observed at very low values of q/sup 2/< or approx. =1 GeV/sup 2/. Limits on the effective QCD scale parameter ..lambda.. and on the magnitude of the twist-4 correction are set. The best fit, neglecting higher-twist contributions, gives ..lambda.. = 92/sub -/36/sup +20/ MeV.
Higuchi, K; Higuchi, M
2007-09-12
We compare the vorticity expansion approximation (VEA) with the local density approximation (LDA) of the current-density functional theory from the viewpoint of sum rules. The VEA formulae satisfy all sum rules which are derived from uniform and nonuniform coordinate scaling properties, while the LDA formulae do not satisfy at least about a third of the sum rules. The validity of the VEA formula is thus confirmed successfully.
Finite-width Laplacian sum rules for 2++ tensor glueball in the instanton vacuum model
NASA Astrophysics Data System (ADS)
Chen, Junlong; Liu, Jueping
2017-01-01
The more carefully defined and more appropriate 2++ tensor glueball current is a S Uc(3 ) gauge-invariant, symmetric, traceless, and conserved Lorentz-irreducible tensor. After Lorentz decomposition, the invariant amplitude of the correlation function is abstracted and calculated based on the semiclassical expansion for quantum chromodynamics (QCD) in the instanton liquid background. In addition to taking the perturbative contribution into account, we calculate the contribution arising from the interaction (or the interference) between instantons and the quantum gluon fields, which is infrared free. Instead of the usual zero-width approximation for the resonances, the Breit-Wigner form with a correct threshold behavior for the spectral function of the finite-width three resonances is adopted. The properties of the 2++ tensor glueball are investigated via a family of the QCD Laplacian sum rules for the invariant amplitude. The values of the mass, decay width, and coupling constants for the 2++ resonance in which the glueball fraction is dominant are obtained.
The sigma meson from QCD sum rules for large-N_c Regge spectra
NASA Astrophysics Data System (ADS)
Afonin, S. S.; Solomko, T. D.
2016-12-01
The QCD sum rules in the large-N_c limit for the light non-strange vector, axial and scalar mesons are considered assuming a string-like linear spectrum for the radially excited states. We propose an improved method for combined analysis of these channels that gives a reasonable description of the observed spectrum. In the vector-axial case, fixing the pion decay constant and the gluon condensate we obtain more or less physical values for the masses of ground states and the quark condensate. Thus a typical need for this method to fix the mass of some ground state is overcome. Using in the scalar channel the values of presumably universal slope of radial trajectories and the quark condensate obtained in the vector-axial channel, we find that, in contrast to some strong claims in the literature, a prediction of light scalar state with a mass close to the mass of f_0(500) seems to be natural in the considered approach and may follow in a natural way from the Regge phenomenology.
Expanded Vandermonde Powers and Sum Rules for the Two-Dimensional One-Component Plasma
NASA Astrophysics Data System (ADS)
Téllez, Gabriel; Forrester, Peter J.
2012-09-01
The two-dimensional one-component plasma (2dOCP) is a system of N mobile particles of the same charge q on a surface with a neutralizing background. The Boltzmann factor of the 2dOCP at temperature T can be expressed as a Vandermonde determinant to the power Γ= q 2/( k B T). Recent advances in the theory of symmetric and anti-symmetric Jack polynomials provide an efficient way to expand this power of the Vandermonde in their monomial basis, allowing the computation of several thermodynamic and structural properties of the 2dOCP for N values up to 14 and Γ equal to 4, 6 and 8. In this work we explore two applications of this formalism, to the study of the pair correlation function of the 2dOCP on the sphere, and the distribution of radial statistics of the 2dOCP in the plane. Also provided is a finite N approximation to the pair correlation on the sphere, and a sum rule for the constant term in the large N expansion of the moments of the density in the plane.
Thermal behavior of Charmonium in the vector channel from QCD sum rules
Dominguez, C. A.; Loewe, M.; Rojas, J. C.; Zhang, Y.
2010-11-12
The thermal evolution of the hadronic parameters of charmonium in the vector channel, i.e. the J/{Psi} resonance mass, coupling (leptonic decay constant), total width, and continuum threshold are analyzed in the framework of thermal Hilbert moment QCD sum rules. The continuum threshold s{sub 0} has the same behavior as in all other hadronic channels, i.e. it decreases with increasing temperature until the PQCD threshold s{sub 0} = 4m{sub Q}{sup 2} is reached at T{approx_equal}1.22T{sub c}(m{sub Q} is the charm quark mass). The other hadronic parameters behave in a very different way from those of light-light and heavy-light quark systems. The J/{Psi} mass is essentially constant in a wide range of temperatures, while the total width grows with temperature up to T{approx_equal}1.04T{sub c} beyond which it decreases sharply with increasing T. The resonance coupling is also initially constant beginning to increase monotonically around T{approx_equal}T{sub c}. This behavior of the total width and of the leptonic decay constant is a strong indication that the J/{Psi} resonance might survive beyond the critical temperature for deconfinement, in agreement with some recent lattice QCD results.
Charmonium in the vector channel at finite temperature from QCD sum rules
Dominguez, C. A.; Loewe, M.; Rojas, J. C.; Zhang, Y.
2010-01-01
Thermal Hilbert moment QCD sum rules are used to obtain the temperature dependence of the hadronic parameters of charmonium in the vector channel, i.e. the J/{psi} resonance mass, coupling (leptonic decay constant), total width, and continuum threshold. The continuum threshold s{sub 0}, which signals the end of the resonance region and the onset of perturbative QCD, behaves as in all other hadronic channels, i.e. it decreases with increasing temperature until it reaches the perturbative QCD threshold s{sub 0}=4m{sub Q}{sup 2}, with m{sub Q} the charm quark mass, at T{approx_equal}1.22T{sub c}. The rest of the hadronic parameters behave very differently from those of light-light and heavy-light quark systems. The J/{psi} mass is essentially constant in a wide range of temperatures, while the total width grows with temperature up to T{approx_equal}1.04T{sub c} beyond which it decreases sharply with increasing T. The resonance coupling is also initially constant and then begins to increase monotonically around T{approx_equal}T{sub c}. This behavior of the total width and of the leptonic decay constant provides a strong indication that the J/{psi} resonance might survive beyond the critical temperature for deconfinement.
XYZ-like spectra from Laplace sum rule at N2LO in the chiral limit
NASA Astrophysics Data System (ADS)
Albuquerque, R.; Narison, S.; Fanomezana, F.; Rabemananjara, A.; Rabetiarivony, D.; Randriamanatrika, G.
2016-12-01
We present new compact integrated expressions of QCD spectral functions of heavy-light molecules and four-quark XY Z-like states at lowest order (LO) of perturbative (PT) QCD and up to d = 8 condensates of the Operator Product Expansion (OPE). Then, by including up to next-to-next leading order (N2LO) PT QCD corrections, which we have estimated by assuming the factorization of the four-quark spectral functions, we improve previous LO results from QCD spectral sum rules (QSSR), on the XY Z-like masses and decay constants which suffer from the ill-defined heavy quark mass. PT N3LO corrections are estimated using a geometric growth of the PT series and are included in the systematic errors. Our optimal results based on stability criteria are summarized in Tables 11-14 and compared, in Sec. 10, with experimental candidates and some LO QSSR results. We conclude that the masses of the XZ observed states are compatible with (almost) pure JPC = 1+±, 0++ molecule or/and four-quark states. The ones of the 1-±, 0-± molecule/four-quark states are about 1.5 GeV above the Yc,b mesons experimental candidates and hadronic thresholds. We also find that the couplings of these exotics to the associated interpolating currents are weaker than that of ordinary D,B mesons (fDD ≈ 10-3f D) and may behave numerically as 1/m¯b3/2 (respectively 1/m¯b) for the 1+, 0+ (respectively 1-, 0-) states which can stimulate further theoretical studies of these decay constants.
B → Vℓ+ℓ- in the Standard Model from light-cone sum rules
NASA Astrophysics Data System (ADS)
Bharucha, Aoife; Straub, David M.; Zwicky, Roman
2016-08-01
We present B q → ρ, B q → ω, B q → K ∗, B s → K ∗ and B s → ϕ form factors from light-cone sum rules (LCSR) at {O}({α}_s) for twist-2 and 3 and {O}({α}_s^0) for twist-4 with updated hadronic input parameters. Three asymptotic light-cone distribution amplitudes of twist-4 (and 5) are determined, necessary for the form factors to obey the equations of motion. It is argued that the latter constrain the uncertainty of tensor-to-vector form factor ratios thereby improving the prediction of zeros of helicity amplitudes of major importance for B → K ∗ℓℓ angular observables. We provide easy-to-use fits to the LCSR results, including the full error correlation matrix, in all modes at low q 2 as well as combined fits to LCSR and lattice results covering the entire kinematic range for B q → K ∗, B s → K ∗ and B s → ϕ. The error correlation matrix avoids the problem of overestimating the uncertainty in phenomenological applications. Using the new form factors and recent computations of non-factorisable contributions we provide Standard Model predictions for B → K ∗γ as well as B → K ∗ℓ+ℓ- and B s → ϕμ + μ - at low dilepton invariant mass. Employing our B → ( ρ,ω) form factor results we extract the CKM element | V ub| from the semileptonic decays B → ( ρ, ω)ℓ ν and find good agreement with other exclusive determinations.
NASA Astrophysics Data System (ADS)
Koretune, Susumu
2007-06-01
The sum rules for the spin dependent structure function g1ab in the null-plane formalism corresponding to the moment at n = 0 has been transformed to the sum rule which relates the g1ab with the cross section of the isovector photon or the real photon. Based on these sum rules, we argue that there is a deep connection among the elastic, the resonance, and the non-resonant contributions, and that it explains why the sign of the generalized Gerasimov-Drell-Hern sum changes at very small Q2.
Unitarity sum rules, three-site moose model, and the ATLAS 2 TeV diboson anomalies
NASA Astrophysics Data System (ADS)
Abe, Tomohiro; Nagai, Ryo; Okawa, Shohei; Tanabashi, Masaharu
2015-09-01
We investigate W' interpretations for the ATLAS 2 TeV diboson anomalies. The roles of the unitarity sum rules, which ensure the perturbativity of the longitudinal vector boson scattering amplitudes, are emphasized. We find the unitarity sum rules and the custodial symmetry are powerful enough to predict various nontrivial relations among W W Z', W Z W', W W h , W W'h and Z Z'h coupling strengths in a model independent manner. We also perform surveys in the general parameter space of W' models and find the ATLAS 2 TeV diboson anomalies may be interpreted as a W' particle of the three-site moose model, i.e., a Kaluza-Klein like particle in a deconstructed extra dimension model. It is also shown that the nonstandard-model-like Higgs boson is favored by the present data to interpret the ATLAS diboson anomalies as the consequences of the W' and Z' bosons.
NASA Astrophysics Data System (ADS)
Yan, Xin-Hu; Ye, Yun-Xiu; Chen, Jian-Ping; Lu, Hai-Jiang; Zhu, Peng-Jia; Jiang, Feng-Jian
2015-07-01
The radiation and ionization energy loss are presented for single arm Monte Carlo simulation for the GDH sum rule experiment in Hall-A at the Jefferson Lab. Radiation and ionization energy loss are discussed for 12C elastic scattering simulation. The relative momentum ratio \\frac{{Δ p}}{p} and 12C elastic cross section are compared without and with radiative energy loss and a reasonable shape is obtained by the simulation. The total energy loss distribution is obtained, showing a Landau shape for 12C elastic scattering. This simulation work will give good support for radiation correction analysis of the GDH sum rule experiment. Supported by National Natural Science Foundation of China (11135002, 11275083), US Department of Energy contract DE-AC05-84ER-40150 under which Jefferson Science Associates operates the Thomas Jefferson National Accelerator Facility and Natural Science Foundation of An'hui Educational Committee (KJ2012B179)
Coulomb Sum Rule for 40Ca, 48Ca, and 56Fe for |q-->|<=550 MeV/c
NASA Astrophysics Data System (ADS)
Meziani, Z. E.; Barreau, P.; Bernheim, M.; Morgenstern, J.; Turck-Chieze, S.; Altemus, R.; McCarthy, J.; Orphanos, L. J.; Whitney, R. R.; Capitani, G. P.; de Sanctis, E.; Frullani, S.; Garibaldi, F.
1984-06-01
Deep-inelastic electron scattering from 40Ca, 48Ca, and 56Fe has been measured at 60°, 90°, and 140° and at inelasticities up to and including the Δ(3, 3) region. Longitudinal response functions in the momentum interval 300 MeV/c<|q-->|<600 MeV/c were extracted. The experimental Coulomb sum rule is observed between the two calcium isotopes.
Magnetic moment of the XQ state with JP C=1+± in light cone QCD sum rules
NASA Astrophysics Data System (ADS)
Agamaliev, A. K.; Aliev, T. M.; Savcı, M.
2017-02-01
The magnetic moments of the recently observed resonance Xb(5568 ) by D0 Collaboration and its partner with charm quark are calculated in the framework of the light cone QCD sum rules, by assuming that these resonances are represented as tetraquark states with quantum numbers JP C=1+±. The magnetic moment can play a critical role in the determination of the quantum numbers, as well as give useful information about the inner structure of these mesons.
Radiative decays of negative parity heavy baryons in the framework of the light cone QCD sum rules
NASA Astrophysics Data System (ADS)
Agamaliev, A. K.; Aliev, T. M.; Savcı, M.
2017-02-01
The transition form factors responsible for the radiative ΣQ →ΛQ γ and ΞQ‧ →ΞQ γ decays of the negative parity baryons are examined within light cone QCD sum rules. The decay widths of the radiative transitions are calculated using the obtained results of the form factors. A comparison of our predictions on decay widths with the corresponding widths of positive parity baryons is given.
B{sub (s)}{yields}S transitions in the light cone sum rules with the chiral current
Sun Yanjun; Li Zuohong; Huang Tao
2011-01-15
We make a QCD light-cone sum rule assessment of B{sub (s)} semileptonic decays to a light scalar meson, B{sub (s)}{yields}Sl{nu}{sub l}, Sll(l=e,{mu},{tau}). Chiral current correlators are used and calculations are performed at leading order in {alpha}{sub s}. Having little knowledge of the ingredients of the scalar mesons, we confine ourself to the two-quark picture for them and work with the two possible scenarios. The resulting sum rules for the form factors receive no contributions from the twist-3 distribution amplitudes, in comparison with the calculation of the conventional light-cone sum rule approach where the twist-3 parts usually play an important role. We specify the range of the squared momentum transfer q{sup 2}, in which the operator product expansion for the correlators remains valid approximately. It is found that the form factors satisfy a relation consistent with the prediction of soft collinear effective theory. In the effective range we investigate behaviors of the form factors and differential decay widths and compare our calculations with the observations from other approaches.
NASA Astrophysics Data System (ADS)
Chen, Wei; Jin, Hong-ying; Kleiv, R. T.; Steele, T. G.; Wang, Meng; Xu, Qing
2013-08-01
QCD sum rules are employed to determine whether the X(3872) can be described as a mixed state that couples to JPC=1++ charmonium hybrid and D¯D* molecular currents. After calculating the mixed correlator of hybrid and molecular currents, we formulate the sum rule in terms of a mixing parameter that interpolates between the pure molecular and hybrid scenarios. As the mixing parameter is increased from the pure molecular case, the predicted mass increases until it reaches a maximum value in good agreement with the X(3872) and the resulting sum-rule analysis appears more robust than the pure molecular case.
Babusci, D.; Giordano, G.; Baghaei, H.; Cichocki, A.; Blecher, M.; Breuer, M.; Commeaux, C.; Didelez, J.P.; Caracappa, A.; Fan, Q.
1995-12-31
Energy weighted integrals of the difference in helicity-dependent photo-production cross sections ({sigma}{sub {1/2}} - {sigma}{sub 3/2}) provide information on the nucleon`s Spin-dependent Polarizability ({gamma}), and on the spin-dependent part of the asymptotic forward Compton amplitude through the Drell-Hearn-Gerasimov (DHG) sum rule. (The latter forms the Q{sup 2}=0 limit of recent spin-asymmetry experiments in deep-inelastic lepton-scattering.) There are no direct measurements of {sigma}{sub {1/2}} or {sigma}{sub 3/2}, for either the proton or the neutron. Estimates from current {pi}-photo-production multipole analyses, particularly for the proton-neutron difference, are in good agreement with relativistic-l-loop Chiral calculations ({chi}PT) for {gamma} but predict large deviations from the DHG sum rule. Either (a) both the 2-loop corrections to the Spin-Polarizability are large and the existing multipoles are wrong, or (b) modifications to the Drell-Hearn-Gerasimov sum rule are required to fully describe the isospin structure of the nucleon. The helicity-dependent photo-reaction amplitudes, for both the proton and the neutron, will be measured at LEGS from pion-threshold to 470 MeV. In these double-polarization experiments, circularly polarized photons from LEGS will be used with SPHICE, a new frozen-spin target consisting of {rvec H} {center_dot} {rvec D} in the solid phase. Reaction channels will be identified in SASY, a large detector array covering about 80% of 4{pi}. A high degree of symmetry in both target and detector will be used to minimize systematic uncertainties.
Analysis of the X(3872), Zc(3900), and Zc(3885) as axial-vector tetraquark states with QCD sum rules
NASA Astrophysics Data System (ADS)
Wang, Zhi-Gang; Huang, Tao
2014-03-01
In this article, we distinguish the charge conjunctions of the interpolating currents, calculate the contributions of the vacuum condensates up to dimension 10 in a consistent way in the operator product expansion, study the masses and pole residues of the JPC=1+± hidden charmed tetraquark states with the QCD sum rules, and explore the energy-scale dependence in detail for the first time. The predictions MX=3.87-0.09+0.09 GeV and MZ=3.91-0.09+0.11 GeV support assigning the X(3872) and Zc(3900) [or Zc(3885)] as the 1++ and 1+- diquark-antidiquark type tetraquark states, respectively.
Correlations and sum rules in a half-space for a quantum two-dimensional one-component plasma
NASA Astrophysics Data System (ADS)
Jancovici, B.; Šamaj, L.
2007-05-01
This paper is the continuation of a previous one (Šamaj and Jancovici, 2007 J. Stat. Mech. P02002); for a nearly classical quantum fluid in a half-space bounded by a plain plane hard wall (no image forces), we had generalized the Wigner Kirkwood expansion of the equilibrium statistical quantities in powers of Planck's constant \\hbar . As a model system for a more detailed study, we consider the quantum two-dimensional one-component plasma: a system of charged particles of one species, interacting through the logarithmic Coulomb potential in two dimensions, in a uniformly charged background of opposite sign, such that the total charge vanishes. The corresponding classical system is exactly solvable in a variety of geometries, including the present one of a half-plane, when βe2 = 2, where β is the inverse temperature and e is the charge of a particle: all the classical n-body densities are known. In the present paper, we have calculated the expansions of the quantum density profile and truncated two-body density up to order \\hbar ^2 (instead of only to order \\hbar as in the previous paper). These expansions involve the classical n-body densities up to n = 4; thus we obtain exact expressions for these quantum expansions in this special case. For the quantum one-component plasma, two sum rules involving the truncated two-body density (and, for one of them, the density profile) have been derived, a long time ago, by using heuristic macroscopic arguments: one sum rule concerns the asymptotic form along the wall of the truncated two-body density; the other one concerns the dipole moment of the structure factor. In the two-dimensional case at βe2 = 2, we now have explicit expressions up to order \\hbar^2 for these two quantum densities; thus we can microscopically check the sum rules at this order. The checks are positive, reinforcing the idea that the sum rules are correct.
NASA Astrophysics Data System (ADS)
Aliev, T. M.; Savcı, M.
2017-01-01
The strong coupling constants of the π and K mesons with negative parity octet baryons are estimated within the light cone QCD sum rules. It is observed that all strong coupling constants, similarly to the case for the positive parity baryons, can be described in terms of three invariant functions, where two of them correspond to the well known F and D couplings in the SU(3)f symmetry, and the third function describes the SU(3)f symmetry violating effects. We compare our predictions on the strong coupling constants of pseudoscalar mesons of negative parity baryons with those corresponding to the strong coupling constants for the positive parity baryons.
NASA Astrophysics Data System (ADS)
Bhattacharya, Tanmoy; Gupta, Rajan; Maltman, Kim
1998-05-01
In light of recent lattice results for the light quark masses ms and mu+md, we reexamine the use of sum rules in the extraction of these quantities, and discuss a number of potential problems with existing analyses. The most important issue is that of the overall normalization of the hadronic spectral functions relevant to the sum rule analyses. We explain why previous treatments, which fix this normalization by assuming complete resonance dominance of the continuum threshold region, can potentially overestimate the resonance contributions to spectral integrals by factors as large as ~5. We propose an alternate method of normalization based on an understanding of the role of resonances in chiral perturbation theory which avoids this problem. The second important uncertainty we consider relates to the physical content of the assumed location s0 of the onset of duality with perturbative QCD. We find that the extracted quark masses depend very sensitively on this parameter. We show that the assumption of duality imposes very severe constraints on the shape of the relevant spectral function in the dual region and present rigorous lower bounds for mu+md as a function of s0 based on a combination of these constraints and the requirement of positivity of ρ5(s). In the extractions of ms, we find that the conventional choice of the value of s0 is not physical. For a more reasonable choice of s0, we are not able to find a solution that is stable with respect to variations of the Borel transform parameter. This problem can, unfortunately, be overcome only if the hadronic spectral function is determined up to significantly larger values of s than is currently possible. Finally, we also estimate the error associated with the convergence of perturbative QCD expressions used in the sum rule analyses. Our conclusion is that, taking all of these issues into account, the resulting sum rule estimates for both mu+md and ms could easily have uncertainties as large as a factor of 2
NASA Astrophysics Data System (ADS)
Ikawa, Shun-ichi; Yamazaki, Shuichi; Kimura, Masao
1981-06-01
Another form of the sum rule for dipolar absorptions has been derived by means of quantum statistics. The difference between this and usually used form results from a quantum effect on the molecular rotational motion. By the joint use of the two forms, average rotational kinetic energies of water molec in the liquid and solid phases and some dipolar molecules in solutions have been estimated. It has been shown that the average rotational kinetic energ larger than the value expected from the classical equipartition rule, with an increase in the hindering potential for the rotational motion of the mole The dipole moments of water molecules in liquid and solid water have been estimated. These are considerably smaller than the gas-phase value.
Energy-weighted sum rules and the analysis of vibrational structure in molecular spectra
NASA Astrophysics Data System (ADS)
Smith, W. L.
2015-10-01
The energy-weighted sum SV = Σn (E‧n - E″m)|<ψ″m|ψ‧n>|2 = <ψ″m|ΔV|ψ″m> for the vibrational potential functions V‧, V″ associated with transitions between two electronic states of diatomic molecular species is investigated and specific formulae are given using Morse functions for V‧ and V″. It is found that these formulae are useful approximations which provide a convenient way to analyse the vibrational structure of real spectra to give estimates of molecular parameters such as the change in internuclear distance accompanying a transition.
OPE, charm-quark mass, and decay constants of D and Ds mesons from QCD sum rules
Lucha, Wolfgang; Melikhov, Dmitri; Simula, Silvano
2011-01-01
We present a sum-rule extraction of the decay constants of the charmed mesons D and Ds from the two-point correlator of pseudoscalar currents. First, we compare the perturbative expansion for the correlator and the decay constant performed in terms of the pole and the running MS¯ masses of the charm quark. The perturbative expansion in terms of the pole mass shows no signs of convergence whereas reorganizing this very expansion in terms of the MS¯ mass leads to a distinct hierarchy of the perturbative expansion. Furthermore, the decay constants extracted from the pole-mass correlator turn out to be considerably smaller than those obtained by means of the MS¯-mass correlator. Second, making use of the OPE in terms of the MS¯ mass, we determine the decay constants of both D and Ds mesons with an emphasis on the uncertainties in these quantities related both to the input QCD parameters and to the limited accuracy of the method of sum rules. PMID:21949465
B{sub s0} meson and the B{sub s0}BK coupling from QCD sum rules
Bracco, M. E.; Nielsen, M.
2010-08-01
We evaluate the mass of the B{sub s0} scalar meson and the coupling constant in the B{sub s0}BK vertex in the framework of QCD sum rules. We consider the B{sub s0} as a tetraquark state to evaluate its mass. We get m{sub B{sub s0}}=(5.85{+-}0.13) GeV, which is in agreement, considering the uncertainties, with predictions supposing it as a bs state or a BK bound state with J{sup P}=0{sup +}. To evaluate the g{sub B{sub s0}BK} coupling, we use the three-point correlation functions of the vertex, considering B{sub s0} as a normal bs state. The obtained coupling constant is: g{sub B{sub s0}BK}=(16.3{+-}3.2) GeV. This number is in agreement with light-cone QCD sum rules calculation. We have also compared the decay width of the B{sub s0}{yields}BK process considering the B{sub s0} to be a bs state and a BK molecular state. The width obtained for the BK molecular state is twice as big as the width obtained for the bs state. Therefore, we conclude that with the knowledge of the mass and the decay width of the B{sub s0} meson, one can discriminate between the different theoretical proposals for its structure.
OPE, charm-quark mass, and decay constants of D and Ds mesons from QCD sum rules.
Lucha, Wolfgang; Melikhov, Dmitri; Simula, Silvano
2011-06-27
We present a sum-rule extraction of the decay constants of the charmed mesons D and Ds from the two-point correlator of pseudoscalar currents. First, we compare the perturbative expansion for the correlator and the decay constant performed in terms of the pole and the running MS¯ masses of the charm quark. The perturbative expansion in terms of the pole mass shows no signs of convergence whereas reorganizing this very expansion in terms of the MS¯ mass leads to a distinct hierarchy of the perturbative expansion. Furthermore, the decay constants extracted from the pole-mass correlator turn out to be considerably smaller than those obtained by means of the MS¯-mass correlator. Second, making use of the OPE in terms of the MS¯ mass, we determine the decay constants of both D and Ds mesons with an emphasis on the uncertainties in these quantities related both to the input QCD parameters and to the limited accuracy of the method of sum rules.
Liégeois, Vincent; Champagne, Benoît; Lazzeretti, Paolo
2008-06-28
Two molecular properties, the nuclear electromagnetic hypershielding (psi(gamma,alphabeta) ('I)) and the gradient of the electric dipole-magnetic dipole polarizability (nabla(Igamma)G(alphabeta) (')), have been calculated using the time-dependent Hartree-Fock method. Provided the Hellmann-Feynman theorem is satisfied, these quantities are equivalent and are related through the nabla(Igamma)G(alphabeta) (')=eZ(I)psi(gamma,alphabeta) ('I) relation, where Z(I) is the atomic number of atom I and e the magnitude of the electron charge. In such a case, the determination of the nuclear electromagnetic hypershielding presents the computational advantage over the evaluation of the gradient of G(alphabeta) (') of requiring only the knowledge of nine mixed second-order derivatives of the density matrix with respect to both electric and magnetic fields (D(alpha,beta)(-omega,omega)) instead of the 3N (N is the number of atoms) derivatives of the density matrix with respect to the Cartesian coordinates (D(Igamma)). It is shown here for the H(2)O(2) molecule that very large basis sets such as the aug-cc-pVQZ or the R12 basis are required to satisfy the Hellmann-Feynman theorem. These basis set requirements have been substantiated by considering the corresponding rototranslational sum rules. The origin dependence of the rototranslational sum rules for the gradient of G(alphabeta) (') has then been theoretically described and verified for the H(2)O(2) molecule.
NASA Astrophysics Data System (ADS)
Tas, Murat; Tanatar, B.
2008-09-01
We calculate the collective excitation modes of strongly coupled bilayer charged Bose systems. We employ the dielectric matrix formulation to study the correlation effects within the random-phase approximation (RPA), the self consistent field approximation Singwi, Tosi, Land, and Sjölander (STLS), and the quasilocalized charge approximation (QLCA), which satisfies the third-frequency-moment (⟨ω3⟩) sum rule. We find that the QLCA predicts a long-wavelength correlation-induced energy gap in the out-of-phase plasmon mode, similar to the situation in electronic bilayer systems. The energy gap and the plasmon density of states are studied as a function of interlayer separation and coupling parameter rs . The results should be helpful for experimental investigations.
A measurement of {alpha}{sub s}(Q{sup 2}) from the Gross Llewellyn Smith sum rule
Harris, D.A.; Auchincloss, P.; Arroyo, C.G.
1995-06-01
The Gross Llewellyn Smith sum rule has been measured at different values of four-momentum transfer squared (Q{sup 2}) by combining the precise CCFR neutrino data with data from other deep-inelastic scattering experiments at lower values of Q{sup 2}. A comparison with the {Omicron} ({alpha}{sub s}{sup 3}) predictions of perturbative QCD yields a determination of {alpha}{sub s} and its dependence on Q{sup 2} in the range 1GeV{sup 2} < Q{sup 2} < 20 GeV{sup 2}. Low Q{sup 2} tests have greater sensitivity to {alpha}{sub s} (M{sub Z}{sup 2}) than high Q{sup 2} tests, since at low Q{sup 2} {alpha}{sub s} is large and changing rapidly.
Fit to the Bjorken, Ellis-Jaffe and Gross-Llewellyn-Smith sum rules in a renormalon based approach
Campanario, Francisco; Pineda, Antonio
2005-09-01
We study the large order behavior in perturbation theory of the Bjorken, Ellis-Jaffe and Gross-Llewellyn-Smith sum rules. In particular, we consider their first infrared renormalons, for which we obtain their analytic structure with logarithmic accuracy and also an approximate determination of their normalization constant. Estimates of higher order terms of the perturbative series are given. The renormalon subtracted scheme is worked out for these observables and compared with experimental data. Overall, good agreement with experiment is found. This allows us to obtain a-circumflex{sub 0} and some higher-twist nonperturbative constants from experiment: a-circumflex 0.141{+-}0.089; f{sub 3,RS}(1 GeV)=-0.124{sub -0.142}{sup +0.137} GeV{sup 2}.
Physicis of Q{sup 2}-dependence in the nucleon`s G{sub 1}(x,Q{sup 2}) structure function sum rule
Ji, X.
1994-10-26
I discuss in this talk the physics of the Q{sup 2} dependence of the G{sub l}(x,Q{sup 2}) structure function sum rule. For Q{sup 2} > 3 GeV{sup 2}, the Q{sup 2} variation is controlled by pure QCD radiative corrections. For 0.5 < Q{sup 2} < 3 GeV{sup 2}, the twist-four contribution becomes significant, but stays perturbative. For Q{sup 2} below {approximately} 0.05, the sum rule is determined by low-energy theorems. The rapid change of the sum rule between 0.05 and 0.5 GeV{sup 2} signals the transition between parton and hadron degrees of freedom.
Kominis, Ioannis
2001-01-01
This thesis presents the results of E-94010, an experiment at Thomas Jefferson National Accelerator Facility (TJNAF) designed to study the spin structure of the neutron at low momentum transfer, and to test the “extended” Gerasimov-Drell-Hearn (GDH) sum rule. The first experiment of its kind, it was performed in experimental Hall-A of TJNAF using a new polarized ^{3}He facility. It has recently been shown that the GDH sum rule and the Bjorken sum rule are both special examples of a more general sum rule that applies to polarized electron scattering off nucleons. This generalized sum rule, due to Ji and Osborne, reduces to the GDH sum rule at Q^{2} = 0 and to the Bjorken sum rule at Q^{2} >> 1 GeV^{2}. By studying the Q^{2} evolution of the extended GDH sum, one learns about the transition from quark-like behavior to hadronic-like behavior. We measured inclusive polarized cross sections by scattering high energy polarized electrons off the new TJNAF polarized ^{3}He target with both longitudinal and transverse target orientations. The high density ^{3}He target, based on optical pumping and spin exchange, was used as an effective neutron target. The target maintained a polarization of about 35% at beam currents as high as 151tA. We describe the precision ^{3}He polarimetry leading to a systematic uncertainty of the target polarization of 4% (relative). A strained GaAs photocathode was utilized in the polarized electron gun, which provided an electron beam with a polarization of about 70%, known to 3% (relative). By using six different beam energies (between 0.86 and 5.06 GeV) and a fixed scattering angle of 15.5°, a wide kinematic coverage was achieved, with 0.02 GeV^{2}< Q^{2} <1 GcV^{2} and 0.5 GeV< W < 2.5 GeV for the squared momentum transfer and invariant mass, respectively. From the measured cross sections we extract the ^{3}He spin structure functions g$3 He
Gubler, Philipp; Yamamoto, Naoki; Hatsuda, Tetsuo; Nishida, Yusuke
2015-05-15
Making use of the operator product expansion, we derive a general class of sum rules for the imaginary part of the single-particle self-energy of the unitary Fermi gas. The sum rules are analyzed numerically with the help of the maximum entropy method, which allows us to extract the single-particle spectral density as a function of both energy and momentum. These spectral densities contain basic information on the properties of the unitary Fermi gas, such as the dispersion relation and the superfluid pairing gap, for which we obtain reasonable agreement with the available results based on quantum Monte-Carlo simulations.
NASA Astrophysics Data System (ADS)
Kamohara, Masumi; Izumi, Yudai; Tanaka, Masafumi; Okamoto, Keiko; Tanaka, Masahito; Kaneko, Fusae; Kodama, Yoko; Koketsu, Toshiyuki; Nakagawa, Kazumichi
2008-10-01
Absorption spectra of thin films of glycine (Gly), alanine (Ala), valine (Val), serine (Ser), leucine (Leu), phenylalanine (Phe) and methinine (Met) were measured in absolute values of absorption cross section σ( E) for the photon energy E from 3 to 250 eV. We translated σ( E) into the optical oscillator strength distribution df/dE and we examined the Thomas-Reiche-Kuhn sum rule [Hirschfelder, J.O., Curtiss, C.F., Bird, R.B., 1954. Molecular Theory of Gases and Liquids. Wiley, New York, p. 890]. We concluded that T-R-K sum rule was correctly applicable for such relatively large size of biomolecules.
First Measurement of the Gerasimov-Drell-Hearn Sum Rule for 1H from 0.7 to 1.8GeV at ELSA
NASA Astrophysics Data System (ADS)
Dutz, H.; Helbing, K.; Krimmer, J.; Speckner, T.; Zeitler, G.; Ahrens, J.; Altieri, S.; Annand, J. R.; Anton, G.; Arends, H.-J.; Beck, R.; Bock, A.; Bradtke, C.; Braghieri, A.; v. Drachenfels, W.; Frommberger, F.; Godo, M.; Goertz, S.; Grabmayr, P.; Hasegawa, S.; Hansen, K.; Harmsen, J.; Heid, E.; Hillert, W.; Holvoet, H.; Horikawa, N.; Iwata, T.; Hoorebeke, L. Van; D'Hose, N.; Jennewein, P.; Kiel, B.; Klein, F.; Kondratiev, R.; Lang, M.; Lannoy, B.; Leukel, R.; Lisin, V.; Menze, D.; Meyer, W.; Michel, T.; Naumann, J.; Panzeri, A.; Pedroni, P.; Pinelli, T.; Preobrajenski, I.; Radtke, E.; Reicherz, G.; Rohlof, C.; Rostomyan, T.; Sauer, M.; Schoch, B.; Schumacher, M.; Tamas, G.; Thomas, A.; van de Vyver, R.; Weihofen, W.; Zapadtka, F.
2003-11-01
To verify the fundamental Gerasimov-Drell-Hearn (GDH) sum rule for the first time experimentally, we measured the helicity dependent total photoabsorption cross section with circularly polarized real photons and longitudinally polarized nucleons in the photon energy range 0.68 1.82GeV with the tagged photon facility at ELSA. The experiment was carried out with a 4π detection system, a circularly polarized tagged photon beam, and a frozen spin polarized proton target. The contribution to the GDH sum rule in this photon energy range is [49.9±2.4(stat)±2.2(syst)] μb.
NASA Astrophysics Data System (ADS)
Corianò, Claudio; Costantini, Antonio; Rose, Luigi Delle; Serino, Mirko
2014-06-01
We discuss the signature of the anomalous breaking of the superconformal symmetry in = 1 super Yang Mills theory, mediated by the Ferrara-Zumino hypercurrent () with two vector () supercurrents () and its manifestation in the anomaly action, in the form of anomaly poles. This allows to investigate in a unified way both conformal and chiral anomalies. The analysis is performed in parallel to the Standard Model, for comparison. We investigate, in particular, massive deformations of the = 1 theory and the spectral densities of the anomaly form factors which are extracted from the components of this correlator. In this extended framework it is shown that all the anomaly form factors are characterized by spectral densities which flow with the mass deformation. In particular, the continuum contributions from the two-particle cuts of the intermediate states turn into poles in the zero mass limit, with a single sum rule satisfied by each component. Non anomalous form factors, instead, in the same anomalous correlators, are characterized by non-integrable spectral densities. These tend to uniform distributions as one moves towards the conformal point, with a clear dual behaviour. As in a previous analysis of the dilaton pole of the Standard Model, also in this case the poles can be interpreted as signaling the exchange of a composite dilaton/axion/dilatino (ADD) multiplet in the effective Lagrangian. The pole-like behaviour of the anomaly form factors is shown to be a global feature of the correlators, present at all energy scales, due to the sum rules. A similar behaviour is shown to be present in the Konishi current, which identifies additional composite states. We conclude that global anomalous currents characterized by a single flow in the perturbative picture always predict the existence of composite interpolating fields. In case of gauging of these currents, as in superconformal theories coupled to gravity, we show that the cancellation of the corresponding anomalies
Detecting Friedel oscillations in ultracold Fermi gases
NASA Astrophysics Data System (ADS)
Riechers, Keno; Hueck, Klaus; Luick, Niclas; Lompe, Thomas; Moritz, Henning
2017-09-01
Investigating Friedel oscillations in ultracold gases would complement the studies performed on solid state samples with scanning-tunneling microscopes. In atomic quantum gases interactions and external potentials can be tuned freely and the inherently slower dynamics allow to access non-equilibrium dynamics following a potential or interaction quench. Here, we examine how Friedel oscillations can be observed in current ultracold gas experiments under realistic conditions. To this aim we numerically calculate the amplitude of the Friedel oscillations which are induced by a potential barrier in a 1D Fermi gas and compare it to the expected atomic and photonic shot noise in a density measurement. We find that to detect Friedel oscillations the signal from several thousand one-dimensional systems has to be averaged. However, as up to 100 parallel one-dimensional systems can be prepared in a single run with present experiments, averaging over about 100 images is sufficient.
The Zb(10 610) and Zb(10 650) as axial-vector tetraquark states in the QCD sum rules
NASA Astrophysics Data System (ADS)
Wang, Zhi-Gang; Huang, Tao
2014-10-01
In this article, we study the axial-vector mesons Zb(10 610) and Zb(10 650) with the Cγμ-Cγ5 type and Cγμ-Cγν type interpolating currents, respectively, by carrying out the operator product expansion to the vacuum condensates up to dimension 10. In calculations, we explore the energy scale dependence of the QCD spectral densities of the hidden bottom tetraquark states in detail for the first time, and suggest a formula μ=√{MX/Y/Z2-(2} with the effective mass Mb=5.13 GeV to determine the energy scales. The numerical results favor assigning the Zb(10 610) and Zb(10 650) as the Cγμ-Cγ5 type and Cγμ-Cγν type hidden bottom tetraquark states, respectively. We obtain the mass of the JPC=1 hidden bottom tetraquark state as a byproduct, which can be compared to the experimental data in the futures. Furthermore, we study the strong decays Zb±(10 610)→ϒπ±,ηbρ± with the three-point QCD sum rules, the decay widths also support assigning the Zb(10 610) as the Cγμ-Cγ5 type hidden bottom tetraquark state.
Reanalysis of the Zc(4020), Zc(4025), Z(4050) and Z(4250) as Tetraquark States with QCD Sum Rules
NASA Astrophysics Data System (ADS)
Wang, Zhi-Gang
2015-04-01
In this article, we calculate the contributions of the vacuum condensates up to dimension-10 in the operator product expansion, and study the Cγμ — Cγν type scalar, axial-vector and tensor tetraquark states in details with the QCD sum rules. In calculations, we use the formula to determine the energy scales of the QCD spectral densities. The predictions MJ=2 = ({4.02}+0.09-0.09)GeV, MJ=1 =(4.02+0.07-0.08)GeV favor assigning the Zc(4020) and Zc(4025) as the JPC = 1+- or 2++ diquark-antidiquark type tetraquark states, while the prediction MJ=0 = (3.85+0.15-0.09)GeV disfavors assigning the Z(4050) and Z(4250) as the JPC = 0++ diquark-antidiquark type tetraquark states. Furthermore, we discuss the strong decays of the 0++, 1+-, 2++ diquark-antidiquark type tetraquark states in details. Supported by National Natural Science Foundation of Chian under Grant No. 11375063, and Natural Science Foundation of Hebei Province under Grant No. A2014502017
NASA Astrophysics Data System (ADS)
Zhou, Juefei
This dissertation combines theoretical and experimental studies of organic molecules to understand light-matter interactions with the goal of making more efficient nonlinear-optical molecules. We use a finite element method to numerically calculate and optimize the nonlinear-optical susceptibilities of 1-dimensional molecules, which resulted in a new paradigm for fabricating molecules with better nonlinear properties. This approach was used as a guide by researchers to identify and characterize a record-high intrinsic hyperpolarizability. Using the results of a sum rule analysis, we propose a new method for modeling the nonlinear-optical spectra of molecules. We apply our theory to the two-photon absorption cross section of the Air Force dye called AF455, and find that it is consistent with our measurements. The properties of the first two excited states of AF455 determined with a combination of linear absorption spectroscopy and hyper-Rayleigh scattering measurements are sufficient to predict, within experimental uncertainty, the full two-photon absorption spectrum.
Precision calculation of threshold πd scattering, πN scattering lengths, and the GMO sum rule
NASA Astrophysics Data System (ADS)
Baru, V.; Hanhart, C.; Hoferichter, M.; Kubis, B.; Nogga, A.; Phillips, D. R.
2011-12-01
We use chiral perturbation theory (ChPT) to calculate the πd scattering length with an accuracy of a few percent, including isospin-violating corrections in both the two- and three-body sectors. In particular, we provide the technical details of a recent letter (Baru et al., 2011) [1], where we used data on pionic deuterium and pionic hydrogen atoms to extract the isoscalar and isovector pion-nucleon scattering lengths a and a. We study isospin-breaking contributions to the three-body part of a due to mass differences, isospin violation in the πN scattering lengths, and virtual photons. This last class of effects is ostensibly infrared enhanced due to the smallness of the deuteron binding energy. However, we show that the leading virtual-photon effects that might undergo such enhancement cancel, and hence the standard ChPT counting provides a reliable estimate of isospin violation in a due to virtual photons. Finally, we discuss the validity of the Goldberger-Miyazawa-Oehme sum rule in the presence of isospin violation, and use it to determine the charged-pion-nucleon coupling constant.
NASA Astrophysics Data System (ADS)
Kumar, Manoj; Banerjee, Varsha; Puri, Sanjay
2017-01-01
We perform comprehensive Monte Carlo (MC) simulations to study ordering dynamics in the random field Ising model with conserved order parameter (C-RFIM) in d=2,3 . The observations from this study are: a) For a fixed value of the disorder Δ, the correlation function C(r,t;Δ) exhibits dynamical scaling. b) The scaling function is not robust with respect to Δ, i.e., super-universality (SU) is violated by C(r,t;Δ) . c) At early times, the domains follow the algebraic growth with a disorder-dependent exponent: L(t,Δ)∼ t1/\\bar{z(Δ)} . At late times, there is a crossover to logarithmic growth: L(t,Δ) ∼ (\\ln t)1/\\varphi , where φ is a disorder-independent exponent. d) The small-r behavior of the correlation function exhibits a cusp singularity: 1-C(r) ∼ rα(Δ) , where α is the cusp exponent signifying rough fractal interfaces. e) The corresponding structure factor exhibits a non-Porod tail: S(k,t;Δ)∼ k-(d+α) , and obeys a generalized Tomita sum rule \\int_0^∞ {d}p p1-α≤ft[pd+αf(p)-C\\right]=0 , where f(p) is the appropriate scaling function, and C is a constant.
Heavy-Light Exotics from QCD Laplace Sum Rule at N2LO in the chiral limit
NASA Astrophysics Data System (ADS)
Albuquerque, R. M.; Fanomezana, F.; Narison, S.; Rabemananjara, A.; Rabetiarivony, D.; Randriamanatrika, G.
2017-01-01
These talks review and summarize our results in [1, 2] on XYZ-like spectra obtained from QCD Laplace Sum Rule in the chiral limit at next-to-next-leading order (N2LO) of perturbation theory (PT) and including leading order (LO) contributions of dimensions d ≤ 6 - 8 non-perturbative condensates. We conclude that the observed XZ states are good candidates for 1+ and 0+ molecules or / and four-quark states while the predictions for 1- and 0- states are about 1.5 GeV above the Yc,b experimental candidates and hadronic thresholds. We (numerically) find that these exotic molecules couple weakly to the corresponding interpolating currents than ordinary D, B heavy-light mesons while we observe that these couplings decrease faster [ 1 /mb3/2 (resp. 1 /mb) for the 1+, 0+ (resp. 1-, 0-) states] than 1 /mb1/2. results do not also confirm the existence of the X(5568) state in agreement with LHCb findings.
NASA Astrophysics Data System (ADS)
Guo, Zhi-Hui; Oller, J. A.; de Elvira, J. Ruiz
2012-09-01
In this work, we perform the one-loop calculation of the scalar and pseudoscalar form factors in the framework of U(3) chiral perturbation theory with explicit tree level exchanges of resonances. The meson-meson scattering calculation from Guo and Oller [Phys. Rev. DPRVDAQ1550-7998 84, 034005 (2011)10.1103/PhysRevD.84.034005] is extended as well. The spectral functions of the nonet scalar-scalar (SS) and pseudoscalar-pseudoscalar (PP) correlators are constructed by using the corresponding form factors. After fitting the unknown parameters to the scattering data, we discuss the resonance content of the resulting scattering amplitudes. We also study spectral-function sum rules in the SS-SS, PP-PP, and SS-PP sectors as well as semilocal duality from scattering. The former relate the scalar and pseudoscalar spectra between themselves while the latter mainly connects the scalar spectrum with the vector one. Finally we investigate these items as a function of NC for NC>3. All these results pose strong constraints on the scalar dynamics and spectroscopy that are discussed. They are successfully fulfilled by our meson-meson scattering amplitudes and spectral functions.
NASA Astrophysics Data System (ADS)
Nath, N. M.; Mukharjee, A.; Das, M. K.; Sarma, J. K.
2016-12-01
We present an analysis of the xF3(x,Q2) structure function and Gross-Llewellyn Smith(GLS) sum rule taking into account the nuclear effects and higher twist correction. This analysis is based on the results presented in [N.M. Nath, et al, Indian J. Phys. 90 (2016) 117]. The corrections due to nuclear effects predicted in several earlier analysis are incorporated to our results of xF3(x,Q2) structure function and GLS sum rule for free nucleon, corrected upto next-next-to-leading order (NNLO) perturbative order and calculate the nuclear structure function as well as sum rule for nuclei. In addition, by means of a simple model we have extracted the higher twist contributions to the non-singlet structure function xF3(x,Q2) and GLS sum rule in NNLO perturbative orders and then incorporated them to our results. Our NNLO results along with nuclear effect and higher twist corrections are observed to be compatible with corresponding experimental data and other phenomenological analysis. Support from DAE-BRNS, India, as Major Research Project under Sanction No. 2012/37P/36/BRNS/2018 dated 24 Nov. 2012
Reconsideration of the B →K* transition form factors within the QCD light-cone sum rules
NASA Astrophysics Data System (ADS)
Cheng, Wei; Wu, Xing-Gang; Fu, Hai-Bing
2017-05-01
In this paper, we study the B →K* transition form factors (TFFs) within the QCD light-cone sum rules (LCSR) approach. Two correlators, i.e., the usual one and the right-handed one, are adopted in the LCSR calculation. The resultant LCSRs for the B →K* TFFs are arranged according to the twist structure of the K*-meson light-cone distribution amplitudes (LCDAs), whose twist-2, twist-3, and twist-4 terms behave quite differently by using different correlators. We observe that the twist-4 LCDAs, though generally small, shall have sizable contributions to the TFFs A1 /2, V , and T1; thus, the twist-4 terms should be kept for a sound prediction. We also observe that, even though different choices of the correlator lead to different LCSRs with different twist contributions, the large correlation coefficients for most of the TFFs indicate that the LCSRs for different correlators are close to each order, not only for their values at the large recoil point q2=0 but also for their ascending trends in the whole q2 region. Such a high degree of correlation is confirmed by their application to the branching fraction of the semileptonic decay B →K*μ+μ- . Thus, a proper choice of correlator may inversely provide a chance for probing uncertain LCDAs; i.e., the contributions from those LCDAs can be amplified to a certain degree via a proper choice of correlator, thus amplifying the sensitivity of the TFFs and, hence, their related observables, to those LCDAs.
Final COMPASS results on the deuteron spin-dependent structure function g1d and the Bjorken sum rule
NASA Astrophysics Data System (ADS)
Adolph, C.; Aghasyan, M.; Akhunzyanov, R.; Alexeev, M. G.; Alexeev, G. D.; Amoroso, A.; Andrieux, V.; Anfimov, N. V.; Anosov, V.; Augsten, K.; Augustyniak, W.; Austregesilo, A.; Azevedo, C. D. R.; Badełek, B.; Balestra, F.; Ball, M.; Barth, J.; Beck, R.; Bedfer, Y.; Bernhard, J.; Bicker, K.; Bielert, E. R.; Birsa, R.; Bodlak, M.; Bordalo, P.; Bradamante, F.; Braun, C.; Bressan, A.; Büchele, M.; Chang, W.-C.; Chatterjee, C.; Chiosso, M.; Choi, I.; Chung, S.-U.; Cicuttin, A.; Crespo, M. L.; Curiel, Q.; Dalla Torre, S.; Dasgupta, S. S.; Dasgupta, S.; Denisov, O. Yu.; Dhara, L.; Donskov, S. V.; Doshita, N.; Dreisbach, Ch.; Duic, V.; Dünnweber, W.; Dziewiecki, M.; Efremov, A.; Eversheim, P. D.; Eyrich, W.; Faessler, M.; Ferrero, A.; Finger, M.; Finger, M.; Fischer, H.; Franco, C.; du Fresne von Hohenesche, N.; Friedrich, J. M.; Frolov, V.; Fuchey, E.; Gautheron, F.; Gavrichtchouk, O. P.; Gerassimov, S.; Giarra, J.; Giordano, F.; Gnesi, I.; Gorzellik, M.; Grabmüller, S.; Grasso, A.; Grosse Perdekamp, M.; Grube, B.; Grussenmeyer, T.; Guskov, A.; Haas, F.; Hahne, D.; Hamar, G.; von Harrach, D.; Heinsius, F. H.; Heitz, R.; Herrmann, F.; Horikawa, N.; d'Hose, N.; Hsieh, C.-Y.; Huber, S.; Ishimoto, S.; Ivanov, A.; Ivanshin, Yu.; Iwata, T.; Jary, V.; Joosten, R.; Jörg, P.; Kabuß, E.; Kerbizi, A.; Ketzer, B.; Khaustov, G. V.; Khokhlov, Yu. A.; Kisselev, Yu.; Klein, F.; Klimaszewski, K.; Koivuniemi, J. H.; Kolosov, V. N.; Kondo, K.; Königsmann, K.; Konorov, I.; Konstantinov, V. F.; Kotzinian, A. M.; Kouznetsov, O. M.; Krämer, M.; Kremser, P.; Krinner, F.; Kroumchtein, Z. V.; Kulinich, Y.; Kunne, F.; Kurek, K.; Kurjata, R. P.; Lednev, A. A.; Lehmann, A.; Levillain, M.; Levorato, S.; Lian, Y.-S.; Lichtenstadt, J.; Longo, R.; Maggiora, A.; Magnon, A.; Makins, N.; Makke, N.; Mallot, G. K.; Marianski, B.; Martin, A.; Marzec, J.; Matoušek, J.; Matsuda, H.; Matsuda, T.; Meshcheryakov, G. V.; Meyer, M.; Meyer, W.; Mikhailov, Yu. V.; Mikhasenko, M.; Mitrofanov, E.; Mitrofanov, N.; Miyachi, Y.; Nagaytsev, A.; Nerling, F.; Neyret, D.; Nový, J.; Nowak, W.-D.; Nukazuka, G.; Nunes, A. S.; Olshevsky, A. G.; Orlov, I.; Ostrick, M.; Panzieri, D.; Parsamyan, B.; Paul, S.; Peng, J.-C.; Pereira, F.; Pešek, M.; Peshekhonov, D. V.; Pierre, N.; Platchkov, S.; Pochodzalla, J.; Polyakov, V. A.; Pretz, J.; Quaresma, M.; Quintans, C.; Ramos, S.; Regali, C.; Reicherz, G.; Riedl, C.; Roskot, M.; Rossiyskaya, N. S.; Ryabchikov, D. I.; Rybnikov, A.; Rychter, A.; Salac, R.; Samoylenko, V. D.; Sandacz, A.; Santos, C.; Sarkar, S.; Savin, I. A.; Sawada, T.; Sbrizzai, G.; Schiavon, P.; Schmidt, K.; Schmieden, H.; Schönning, K.; Seder, E.; Selyunin, A.; Silva, L.; Sinha, L.; Sirtl, S.; Slunecka, M.; Smolik, J.; Srnka, A.; Steffen, D.; Stolarski, M.; Subrt, O.; Sulc, M.; Suzuki, H.; Szabelski, A.; Szameitat, T.; Sznajder, P.; Takekawa, S.; Tasevsky, M.; Tessaro, S.; Tessarotto, F.; Thibaud, F.; Thiel, A.; Tosello, F.; Tskhay, V.; Uhl, S.; Vauth, A.; Veloso, J.; Virius, M.; Vondra, J.; Wallner, S.; Weisrock, T.; Wilfert, M.; Windmolders, R.; ter Wolbeek, J.; Zaremba, K.; Zavada, P.; Zavertyaev, M.; Zemlyanichkina, E.; Zhuravlev, N.; Ziembicki, M.; Zink, A.
2017-06-01
Final results are presented from the inclusive measurement of deep-inelastic polarised-muon scattering on longitudinally polarised deuterons using a 6LiD target. The data were taken at 160 GeV beam energy and the results are shown for the kinematic range 1(GeV / c) 2
Phase Shift of the Asymmetric Friedel-Anderson Impurity
NASA Astrophysics Data System (ADS)
Bergmann, Gerd
2013-04-01
The ground state of the asymmetric Friedel-Anderson (aFA) impurity is calculated within the FAIR (Friedel artificially inserted resonance) theory. Its properties are investigated by means of the fidelity with different Friedel impurities and by its Friedel oscillations. Friedel impurities with a specific phase shift δ at the Fermi level possess a finite fidelity with the aFA impurity. This phase shift δ determines other properties of the aFA impurity such as the amplitude and displacement of its Friedel oscillations. One can find the parameters of a Friedel impurity which coincides in its Friedel oscillations almost perfectly with the aFA impurity, thereby avoiding an Anderson orthogonality catastrophe.
NASA Astrophysics Data System (ADS)
Nath, N. M.; Sarma, J. K.
2017-05-01
A calculation of the non-singlet part of spin dependent structure function, xg1^{NS}(x,Q2) and associated sum rule, the Bjorken Sum rule up to next-next-to-leading order(NNLO) is presented. We use a unified approach incorporating Regge theory and the theoretical framework of perturbative Quantum Chromodynamics. Using a Regge behaved model with Q 2 dependent intercept as the initial input, we have solved the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equation up to NNLO at small- x for xg1^{NS}(x,Q2) and the solutions are utilised to calculate the polarised Bjorken sum rule(BSR). We have also extracted the higher twist contribution to BSR based on a simple parametrisation. These results for both of xg1^{NS}(x,Q2) and BSR, along with higher twist corrections are observed to be consistent with the available data taken from SMC, E143, HERMES, COMPASS and JLab experiments. In addition, our results are also compared with that of other theoretical and phenomenological analysis based on different models and a very good agreement is also observed in this regard. Further a very good consistency between our calculated results and theoretical QCD predictions of BSR is also achieved.
g{sub {Sigma}{sub Q{Sigma}{sub Q{pi}}}}coupling constant via light cone QCD sum rules
Azizi, K.; Bayar, M.; Ozpineci, A.; Sarac, Y.
2010-10-01
Using the most general form of the interpolating currents, the coupling constants g{sub {Sigma}{sub b{Sigma}{sub b{pi}}}}and g{sub {Sigma}{sub c{Sigma}{sub c{pi}}}}are calculated within the light cone QCD sum rules approach. It is found that g{sub {Sigma}{sub c{Sigma}{sub c{pi}=}}}-8.0{+-}1.7 and g{sub {Sigma}{sub b{Sigma}{sub b{pi}=}}}-11.0{+-}2.1.
NASA Technical Reports Server (NTRS)
Ying, Hao
1993-01-01
The fuzzy controllers studied in this paper are the ones that employ N trapezoidal-shaped members for input fuzzy sets, Zadeh fuzzy logic and a centroid defuzzification algorithm for output fuzzy set. The author analytically proves that the structure of the fuzzy controllers is the sum of a global nonlinear controller and a local nonlinear proportional-integral-like controller. If N approaches infinity, the global controller becomes a nonlinear controller while the local controller disappears. If linear control rules are used, the global controller becomes a global two-dimensional multilevel relay which approaches a global linear proportional-integral (PI) controller as N approaches infinity.
Bobrov, V. B.
2011-03-15
In the context of the electron-ion interaction potential, a rigorous description is given of the permittivity {epsilon}({omega}) of a fully ionized plasma in the frequency range {omega} Much-Greater-Than v-tilde{sub ei}, where v{sub ei} is the characteristic electron-ion collision frequency. The interaction and degeneration effects in the electron and ion subsystems are systematically taken into account. The asymptotics of the effective collision frequency {nu}({omega}) and the renormalization function {gamma}({omega}) for the plasma frequency are found, and the rules of sums for the permittivity {epsilon}({omega}) are determined.
In vitro evolution of a Friedel-Crafts deoxyribozyme.
Mohan, Utpal; Burai, Ritwik; McNaughton, Brian R
2013-04-14
We report the in vitro selection of a single-stranded 72-nucleotide DNA enzyme (deoxyribozyme) that catalyzes a Friedel-Crafts reaction between an indole and acyl imidazole in good yield and in aqueous solvent. Appreciable Friedel-Crafts product requires addition of copper nitrate and the deoxyribozyme. We observe deoxyribozyme-mediated bond formation for both in cis and in trans Friedel-Crafts reactions.
NASA Astrophysics Data System (ADS)
Cvetič, Gorazd; Kataev, A. L.
2016-07-01
We consider a new form of analytical perturbation theory expansion in the massless S U (Nc) theory, for the nonsinglet part of the e+e--annihilation to hadrons Adler function Dn s and of the Bjorken sum rule of the polarized lepton-hadron deep-inelastic scattering Cns B j p, and demonstrate its validity at the O (αs4)-level at least. It is a two-fold series in powers of the conformal anomaly and of S U (Nc) coupling αs. Explicit expressions are obtained for the {β }-expanded perturbation coefficients at O (αs4) level in MS ¯ scheme, for both considered physical quantities. Comparisons of the terms in the {β }-expanded coefficients are made with the corresponding terms obtained by using extra gluino degrees of freedom, or skeleton-motivated expansion, or Rδ-scheme motivated expansion in the Principle of Maximal Conformality. Relations between terms of the {β }-expansion for the Dn s- and Cns B j p-functions, which follow from the conformal symmetry limit and its violation, are presented. The relevance to the possible new analyses of the experimental data for the Adler function and Bjorken sum rule is discussed.
NASA Astrophysics Data System (ADS)
Kumar, Ashok; Thakkar, Ajit J.
2010-02-01
The construction of the dipole oscillator strength distribution (DOSD) from theoretical and experimental photoabsorption cross sections combined with constraints provided by the Kuhn-Reiche-Thomas sum rule and molar refractivity data is a well-established technique that has been successfully applied to more than 50 species. Such DOSDs are insufficiently accurate at large photon energies. A novel iterative procedure is developed that rectifies this deficiency by using the high-energy asymptotic behavior of the dipole oscillator strength density as an additional constraint. Pilot applications are made for the neon, argon, krypton, and xenon atoms. The resulting DOSDs improve the agreement of the predicted S2 and S1 sum rules with ab initio calculations while preserving the accuracy of the remainder of the moments. Our DOSDs exploit new and more accurate experimental data. Improved estimates of dipole properties for these four atoms and of dipole-dipole C6 and triple-dipole C9 dispersion coefficients for the interactions among them are reported.
NASA Astrophysics Data System (ADS)
Zhang, J.-Z.; Galbraith, I.
2008-05-01
Using perturbation theory, intraband magneto-optical absorption is calculated for InAs/GaAs truncated pyramidal quantum dots in a magnetic field applied parallel to the growth direction z . The effects of the magnetic field on the electronic states as well as the intraband transitions are systematically studied. Selection rules governing the intraband transitions are discussed based on the symmetry properties of the electronic states. While the broadband z -polarized absorption is almost insensitive to the magnetic field, the orbital Zeeman splitting is the dominant feature in the in-plane polarized spectrum. Strong in-plane polarized magneto-absorption features are located in the far-infrared region, while z -polarized absorption occurs at higher frequencies. This is due to the dot geometry (the base length is much larger than the height) yielding different quantum confinement in the vertical and lateral directions. The Thomas-Reiche-Kuhn sum rule, including the magnetic field effect, is applied together with the selection rules to the absorption spectra. The orbital Zeeman splitting depends on both the dot size and the confining potential—the splitting decreases as the dot size or the confining potential decreases. Our calculated Zeeman splittings are in agreement with experimental data.
Jeffries, J R; Moore, K T; Butch, N P; Maple, M B
2010-05-19
We examine the degree of 5f electron localization in URu{sub 2}Si{sub 2} using spin-orbit sum rule analysis of the U N{sub 4,5} (4d {yields} 5f) edge. When compared to {alpha}-U metal, US, USe, and UTe, which have increasing localization of the 5f states, we find that the 5f states of URu{sub 2}Si{sub 2} are more localized, although not entirely. Spin-orbit analysis shows that intermediate coupling is the correct angular momentum coupling mechanism for URu{sub 2}Si{sub 2} when the 5f electron count is between 2.6 and 2.8. These results have direct ramifications for theoretical assessment of the hidden order state of URu{sub 2}Si{sub 2}, where the degree of localization of the 5f electrons and their contribution to the Fermi surface are critical.
A QCD sum rules calculation of the ηcD*D and ηc Ds* Ds form factors and strong coupling constants
NASA Astrophysics Data System (ADS)
Rodrigues, B. Osório; Bracco, M. E.; Zanetti, C. M.
2017-10-01
We use the QCD sum rules for the three point correlation functions to compute the strong coupling constants of the meson vertices ηcD* D and ηc Ds* Ds. We consider perturbative and non-perturbative contributions, working up to dimension five on the OPE. The vertices were studied considering that each one of its three mesons are off-shell alternately. The vertex coupling constant is evaluated through the extrapolation of the three different form factors. The results obtained for the coupling constants are gηcD*D =5.23-1.38+1.80 and g ηc Ds* Ds =5.55-1.55+1.29.
Analysis of the strong coupling form factors of ΣbNB and ΣcND in QCD sum rules
NASA Astrophysics Data System (ADS)
Yu, Guo-Liang; Wang, Zhi-Gang; Li, Zhen-Yu
2017-08-01
In this article, we study the strong interaction of the vertices Σ b NB and Σ c ND using the three-point QCD sum rules under two different Dirac structures. Considering the contributions of the vacuum condensates up to dimension 5 in the operation product expansion, the form factors of these vertices are calculated. Then, we fit the form factors into analytical functions and extrapolate them into time-like regions, which gives the coupling constants. Our analysis indicates that the coupling constants for these two vertices are G ΣbNB = 0.43±0.01 GeV-1 and G ΣcND = 3.76±0.05 GeV-1. Supported by Fundamental Research Funds for the Central Universities (2016MS133)
Friedel oscillations as a probe of fermionic quasiparticles
NASA Astrophysics Data System (ADS)
Dalla Torre, Emanuele G.; Benjamin, David; He, Yang; Dentelski, David; Demler, Eugene
2016-05-01
When immersed in a sea of electrons, local impurities give rise to density modulations known as Friedel oscillations. In spite of the generality of this phenomenon, the exact shape of these modulations is usually computed only for noninteracting electrons with a quadratic dispersion relation. In actual materials, Friedel oscillations are a viable way to access the properties of electronic quasiparticles, including their dispersion relation, lifetime, and pairing. In this work we analyze the signatures of Friedel oscillations in STM and x-ray scattering experiments, focusing on the concrete example of cuprate superconductors. We identify signatures of Friedel oscillations seeded by impurities and vortices, and explain experimental observations that have been previously attributed to a competing charge order.
NASA Astrophysics Data System (ADS)
Bakulev, A. P.; Mikhailov, S. V.; Pimikov, A. V.; Stefanis, N. G.
2011-10-01
A global fit to the data from different collaborations (CELLO, CLEO, BaBar) on the pion-photon transition form factor is carried out using light-cone sum rules. The analysis includes the next-to-leading QCD radiative corrections and the twist-four contributions, while the main next-to-next-to-leading term and the twist-six contribution are taken into account in the form of theoretical uncertainties. We use the information extracted from the data to investigate the pivotal characteristics of the pion distribution amplitude. This is done by dividing the data into two sets: one containing all data up to 9 GeV 2, whereas the other incorporates also the high- Q tail of the BaBar data. We find that it is not possible to accommodate into the fit these BaBar data points with the same accuracy and conclude that it is difficult to explain these data in the standard scheme of OCD.
NASA Astrophysics Data System (ADS)
Levchuk, M. I.
2010-10-01
Helicity-dependent incoherent pion photoproduction in the reaction γ⃗d⃗→πNN is studied in the framework of the diagrammatic approach. Contributions to the reaction amplitude from diagrams corresponding to impulse approximation as well as NN and πN interactions in the final state have been evaluated. The elementary γN→πN operator is taken from the MAID and SAID models. A detailed comparison of the predictions with recent experimental data by the GDH and A2 collaborations at energies below 500 MeV is presented. Reasonable agreement with the data on the yields and cross sections for the polarized beam and polarized target has been achieved in all channels. The unpolarized data of the GDH and A2 collaborations have also been analyzed within the approach. A strong overestimation for the neutral channel has been found. At the same time, the model provides a quite satisfactory description of the unpolarized data for the charged channels. The sensitivity of the obtained results to the choice of the elementary γN→πN operator is discussed in detail. The contribution of the γd→πNN reaction to the GDH sum rule for the deuteron up to a photon energy of 1.65 GeV has been evaluated with the result of 235±25 μb.
NASA Astrophysics Data System (ADS)
Grebennikov, Vladimir I.; Bebenin, Nikolai G.; Zainullina, Rimma I.; Kuepper, Karsten; Kuznetsova, Tatyana V.
2017-10-01
The problem of determining the magnitude of the atomic magnetic moments in compounds with rare-earth and transition elements using the X-ray magnetic circular dichroism (XMCD) is investigated. The standard sum rules approach usually gives the moment values by several times smaller than their bulk values obtained from the direct magnetic measurements. We attribute this to the strong spin fluctuations in the surface layer which actually formed the soft XMCD signal. A method of determining the value of the local magnetic moments in the presence of strong fluctuations is proposed. The magnetic interactions in La0.5Pr0.2Ca0.3MnO3 are investigated by x-ray absorption spectroscopy, XMCD and bulk magnetization measurements. The proposed procedure is used to determine the values of atomic magnetic moments of transition and rare-earth elements as well as net magnetization on the surface and in the bulk from experimental Mn L2,3 and Pr M4,5 XMCD spectra.
Study of D →a0(980 )e+νe decay in the light-cone sum rules approach
NASA Astrophysics Data System (ADS)
Cheng, Xiao-Dong; Li, Hai-Bo; Wei, Bin; Xu, Yu-Guo; Yang, Mao-Zhi
2017-08-01
Within the QCD light-cone sum rule (LCSR) approach, we investigate the transition form factors of D →a0(980 ) up to the twist-3 light-cone distribution amplitudes (LCDAs) of the scalar meson a0(980 ) in the two-quark picture. Using these form factors, we calculate the differential decay widths and branching ratios of the D →a0(980 )e+νe semileptonic decays. We obtain B (D0→a0-(980 )e+νe)=(4.0 8-1.22+1.37)×10-4 and B (D+→a00(980 )e+νe)=(5.4 0-1.59+1.78)×10-4 . The results are sensitive to the a0(980 ) inner structure. These decays can be searched for at the BESIII experiment, and any experimental observations will be useful to identify internal quark contents of the a0(980 ) meson, which will shed light on understanding theoretical models.
NASA Astrophysics Data System (ADS)
Mikhailov, S. V.; Pimikov, A. V.; Stefanis, N. G.
2016-06-01
We consider the calculation of the pion-photon transition form factor Fγ*γπ0(Q2) within light-cone sum rules focusing attention to the low-mid region of momenta. The central aim is to estimate the theoretical uncertainties which originate from a wide variety of sources related to (i) the relevance of next-to-next-to-leading order radiative corrections (ii) the influence of the twist-four and the twist-six term (iii) the sensitivity of the results on auxiliary parameters, like the Borel scale M2, (iv) the role of the phenomenological description of resonances, and (v) the significance of a small but finite virtuality of the quasireal photon. Predictions for Fγ*γπ0(Q2) are presented which include all these uncertainties and found to comply within the margin of experimental error with the existing data in the Q2 range between 1 and 5 GeV2 , thus justifying the reliability of the applied calculational scheme. This provides a solid basis for confronting theoretical predictions with forthcoming data bearing small statistical errors.
NASA Astrophysics Data System (ADS)
He, Xiao-Gang; Li, Siao-Fong; Ren, Bo; Yuan, Xing-Bo
2017-09-01
Recent LHCb data for time-dependent C P violation in B0→π+π- and Bs0→K+K- show deviations from theoretical predictions. Besides their central values for CK+K-, SK+K- and AK+K- Δ Γ violate quantum mechanic C P T invariant sum rule (C P T sum rule) prediction of |CK+K-|2+|SK+K-|2+|AK+K- Δ Γ|2=1 (LHCb data imply the sum to be 0.67 ±0.20 .), their values for CK+K-=0.24 ±0.06 ±0.02 and Cπ+π-=-0.24 ±0.07 ±0.01 also show large violation of SU(3) or its U-spin sub-group symmetry (SU (3 )/U ) relation CK+K-/Cπ-π+=-B ¯(B0→π-π+)τBs0/B ¯(Bs0→K+K-)τB0 (LHCb data imply the ratio of left-side to right-side to be 4.67 ±1.88 .). The LHCb results need to be further confirmed to be taken seriously. We suggest to use time-dependent C P violation in Bs→K0K¯0,π+π-,π0π0 to further test the C P T sum rule. Assuming that the sum rule holds, we propose that violation of the SU (3 )/U relation may indicate a large FSI phase difference in the π+π- and K+K- rescattering. We suggest several other U-spin pairs of B →P P decays to further test SU (3 )/U relations.
Friedel-Crafts amidoalkylation via thermolysis and oxidative photocatalysis.
Dai, Chunhui; Meschini, Francesco; Narayanam, Jagan M R; Stephenson, Corey R J
2012-05-04
Friedel-Crafts amidoalkylation was achieved by oxidation of dialkylamides using persulfate (S(2)O(8)(2-)) in the presence of the visible light catalyst, Ru(bpy)(3)Cl(2), at room temperature, via a reactive N-acyliminium intermediate. Alternatively, mild heating of the dialkylamides and persulfate afforded a metal and Lewis acid-free Friedel-Crafts amidoalkylation. Alcohols and electron-rich arenes served as effective nucleophiles, forming new C-O or C-C bonds. In general, photocatalysis provided higher yields and better selectivities.
Friedel-Crafts Amidoalkylation via Thermolysis and Oxidative Photocatalysis
Dai, Chunhui; Meschini, Francesco; Narayanam, Jagan M. R.; Stephenson, Corey R. J.
2012-01-01
Friedel-Crafts amidoalkylation was achieved by oxidation of dialkylamides using persulfate (S2O82−) in the presence of the visible light catalyst, Ru(bpy)3Cl2, at room temperature, via a reactive N-acyliminium intermediate. Alternatively, mild heating of the dialkylamides and persulfate afforded a metal and Lewis acid-free Friedel-Crafts amidoalkylation. Alcohols and electron–rich arenes served as effective nucleophiles, forming new C–O or C–C bonds. In general, photocatalysis provided higher yields and better selectivities. PMID:22458307
The Friedel-Crafts Reaction - A Sixth Form Project
ERIC Educational Resources Information Center
Hodson, D.
1973-01-01
Suggests that the Friedel-Crafts reaction, used for synthesizing a wide range of aromatic compounds, is an ideal vehicle for extended senior high school project work in chemistry. Provides a theoretical discussion of the reaction, suggests a number of suitable investigations, and outlines the experimental details. (JR)
Screening effects and Friedel oscillations in quantum-well nanostructures
Kovalev, V. M.; Chaplik, A. V.
2008-11-15
The screening of the Coulomb interaction is studied with regard to Friedel oscillations in multicomponent electron plasma structure. A double quantum well (QW) and a superlattice are considered. The groundstate energy of a donor (exciton) in a double quantum well is calculated by a variational method as a function of the population of subbands.
Sundu, Hayriye; Bayar, Melahat; Azizi, Kazem
2010-12-22
The form factors of the semileptonic B{sub c{yields}}S(AV)l{nu} (l = {tau},{mu},e) transitions, where S and AV denote the scalar {Chi}{sub c0} and axial vector ({Chi}{sub c1},h{sub c}) mesons, are calculated within the framework of the three-point QCD sum rules. The results of form factors are used to estimate the total decay widths and branching ratios of these transitions. A comparison of our results on branching ratios with the predictions of other approaches is also presented.
Aydin, C.; Bayar, M.; Yilmaz, A. H.
2007-04-23
The coupling constants of {alpha}0 {yields} {omega}{gamma}, f0 {yields} {omega}{gamma}, {alpha}0 {yields} {rho}{gamma}, and f0 {yields} {rho}{gamma} are calculated using 3-point QCD sum rules. We estimate the coupling constants g{alpha}0{omega}{gamma}, gf0{omega}{gamma}, g{alpha}0{rho}{gamma} and gf0{rho}{gamma} which are an essential ingredient in the analysis of physical processes involving isoscalar f0(980) and isovector {alpha}0(980) mesons.
Aydin, C.; Bayar, M.; Yilmaz, A.H.
2006-04-01
The coupling constant of a{sub 0}{yields}{rho}{gamma} and f{sub 0}{yields}{rho}{gamma} decays are calculated using 3-point QCD sum rules. We estimate the coupling constant g{sub a{sub 0}}{sub {rho}}{sub {gamma}} and g{sub f{sub 0}}{sub {rho}}{sub {gamma}} which are an essential ingredient in the analysis of physical processes involving isoscalar f{sub 0}(980) and isovector a{sub 0}(980) mesons.
Friedel oscillations and quasiparticle interference: Complementary STM and REXS approach
NASA Astrophysics Data System (ADS)
Aynajian, Pegor; Gyenis, András; da Silva Neto, Eduardo; He, Feizhou; Sutarto, Ronny; Schierle, Enrico; Weschke, Eugen; Kavai, Mariam; Baumbach, Ryan; Thompson, Joe; Bauer, Eric; Fisk, Zachary; Damascelli, Andrea; Yazdani, Ali
The origin of a competing charge ordering in the high-temperature superconducting cuprates has recently been subject to intense experimental and theoretical debates. Dalla Torre et al theoretically proposed that Friedel oscillations can reproduce the experimentally observed scattering peak in the resonant elastic x-ray scattering (REXS) of cuprates [NJP, 17 022001 2015]. Using complementary spectroscopic imaging with the scanning tunneling microscope and REXS on the heavy fermion compound CeMIn5 (M =Co, Rh) we observe a scattering peak in REXS, similar, yet broader than that found in cuprates. Through temperature and doping dependent experiments, we demonstrate this enhanced peak to originate from the scattering of hybridized heavy f-electrons. We discuss the origin of this phenomenon and its relation to Friedel oscillations and charge ordering.
Extension of Friedel's law to vortex-beam diffraction
NASA Astrophysics Data System (ADS)
Juchtmans, Roeland; Guzzinati, Giulio; Verbeeck, Jo
2016-09-01
Friedel's law states that the modulus of the Fourier transform of real functions is centrosymmetric, while the phase is antisymmetric. As a consequence of this, elastic scattering of plane-wave photons or electrons within the first-order Born-approximation, as well as Fraunhofer diffraction on any aperture, is bound to result in centrosymmetric diffraction patterns. Friedel's law, however, does not apply for vortex beams, and centrosymmetry in general is not present in their diffraction patterns. In this work we extend Friedel's law for vortex beams by showing that the diffraction patterns of vortex beams with opposite topological charge, scattered on the same two-dimensional potential, always are centrosymmetric to one another, regardless of the symmetry of the scattering object. We verify our statement by means of numerical simulations and experimental data. Our research provides deeper understanding in vortex-beam diffraction and can be used to design new experiments to measure the topological charge of vortex beams with diffraction gratings or to study general vortex-beam diffraction.
Gan Longfei; Huang Mingqiu
2010-09-01
We present an analysis of semileptonic decays of orbitally, P-wave excited B{sub s} meson states B{sub s}**, including the newly found narrow B{sub s1}(5830) and B{sub s2}*(5840) states, into low-lying D{sub s} mesons (D{sub s}(1968), D{sub s}*(2112), D{sub sJ}(2317), D{sub sJ}(2460)) within the framework of the heavy quark effective theory. The relevant universal form factors are estimated using QCD sum rules at the leading order of the heavy quark expansion. The decay widths are predicted and the branching ratios are estimated.
Djawotho, Pibero
2002-12-01
This dissertation presents results of experiment E94-010 performed at Jefferson Laboratory (simply known as JLab) in Hall A. The experiment aimed to measure the low Q^{2} evolution of the Gerasimov-Drell-Hearn (GDH) integral from Q^{2} = 0.1 to 0.9 GeV^{2}. The GDH sum rule at the real photon point provides an important test of Quantum Chromodynamics (QCD). The low Q^{2} evolution of the GDH integral contests various resonance models, Chiral Perturbation Theory ({chi} PT) and lattice QCD calculations, but more importantly, it helps us understand the transition between partonic and hadronic degrees of freedom. At high Q^{2}, beyond 1 GeV^{2}, the difference of the GDH integrals for the proton and the neutron is related to the Bjorken sum rule, another fundamental test of QCD. In addition, results of the measurements for the spin structure functions g_{1} and g_{2}, cross sections, and asymmetries are presented. E94-010 was the first experiment of its kind at JLab. It used a high-pressure, polarized ^{3}He target with a gas pressure of 10 atm and average target polarization of 35%. For the first time, the polarized electron source delivered an average beam polarization of 70% with a beam current of 15 micro A. The limit on the beam current was only imposed by the target. The experiment required six different beam energies from 0.86 to 5.1 GeV. This was the first time the accelerator ever reached 5.1 GeV. Both High-Resolution Spectrometers of Hall A, used in singles mode, were positioned at 15.5 ° each.
NASA Astrophysics Data System (ADS)
Blümlein, Johannes; Falcioni, Giulio; De Freitas, Abilio
2016-09-01
We calculate analytically the flavor non-singlet O (αs2) massive Wilson coefficients for the inclusive neutral current non-singlet structure functions F1,2,Lep (x ,Q2) and g1,2ep (x ,Q2) and charged current non-singlet structure functions F1,2,3ν (ν bar) p (x ,Q2), at general virtualities Q2 in the deep-inelastic region. Numerical results are presented. We illustrate the transition from low to large virtualities for these observables, which may be contrasted to basic assumptions made in the so-called variable flavor number scheme. We also derive the corresponding results for the Adler sum rule, the unpolarized and polarized Bjorken sum rules and the Gross-Llewellyn Smith sum rule. There are no logarithmic corrections at large scales Q2 and the effects of the power corrections due to the heavy quark mass are of the size of the known O (αs4) corrections in the case of the sum rules. The complete charm and bottom corrections are compared to the approach using asymptotic representations in the region Q2 ≫mc,b2. We also study the target mass corrections to the above sum rules.
Friedel-Crafts Hydroxyalkylation of Indoles Mediated by Trimethylsilyl Trifluoromethanesulfonate.
Downey, C Wade; Poff, Christopher D; Nizinski, Alissa N
2015-10-16
Indoles and N-alkylindoles undergo Friedel-Crafts addition to aldehydes in the presence of trimethylsilyl trifluoromethanesulfonate and a trialkylamine to produce 3-(1-silyloxyalkyl)indoles. Neutralization of the reaction mixture with pyridine followed by deprotection under basic conditions with tetrabutylammonium fluoride provides the 1:1 adduct as the free alcohol. This method prevents spontaneous conversion of the desired products to the thermodynamically favored bisindolyl(aryl)methanes, a process typically observed when indoles are reacted with aldehydes under acidic conditions.
Accelerated carbonation of Friedel's salt in calcium aluminate cement paste
Goni, S.; Guerrero, A
2003-01-01
The stability of Friedel's salt with respect to carbonation has been studied in calcium aluminate cement (CAC) pastes containing NaCl (3% of Cl{sup -} by weight of cement). Carbonation was carried out on a powdered sample in flowing 5% CO{sub 2} gas at 65% relative humidity to accelerate the process. At an intermediate carbonation step, a part of the sample was washed and dried up to 10 cycles to simulate a dynamic leaching attack. The two processes were followed by means of X-ray diffraction (XRD), pH and Cl{sup -} analyses in the simulated pore solution.
NASA Astrophysics Data System (ADS)
Zhang, J.-Z.; Dyson, A.; Ridley, B. K.
2015-01-01
Using the dielectric continuum (DC) and three-dimensional phonon (3DP) models, energy relaxation (ER) of the hot electrons in the quasi-two-dimensional channel of lattice-matched InAlN/AlN/GaN heterostructures is studied theoretically, taking into account non-equilibrium polar optical phonons, electron degeneracy, and screening from the mobile electrons. The electron power dissipation (PD) and ER time due to both half-space and interface phonons are calculated as functions of the electron temperature Te using a variety of phonon lifetime values from experiment, and then compared with those evaluated by the 3DP model. Thereby, particular attention is paid to examination of the 3DP model to use for the hot-electron relaxation study. The 3DP model yields very close results to the DC model: With no hot phonons or screening, the power loss calculated from the 3DP model is 5% smaller than the DC power dissipation, whereas slightly larger 3DP power loss (by less than 4% with a phonon lifetime from 0.1 to 1 ps) is obtained throughout the electron temperature range from room temperature to 2500 K after including both the hot-phonon effect (HPE) and screening. Very close results are obtained also for ER time with the two phonon models (within a 5% of deviation). However, the 3DP model is found to underestimate the HPE by 9%. The Mori-Ando sum rule is restored by which it is proved that the PD values obtained from the DC and 3DP models are in general different in the spontaneous phonon emission process, except when scattering with interface phonons is sufficiently weak, or when the degenerate modes condition is imposed, which is also consistent with Register's scattering rate sum rule. The discrepancy between the DC and 3DP results is found to be caused by how much the high-energy interface phonons contribute to the ER: their contribution is enhanced in the spontaneous emission process but is dramatically reduced after including the HPE. Our calculation with both phonon
NASA Astrophysics Data System (ADS)
Bullington, Grady D.
2007-01-01
The Connell sum sequence refers to the partial sums of the Connell sequence. In this paper, the Connell sequence, Connell sum sequence and generalizations from Iannucci and Mills-Taylor are interpreted as sums of elements of triangles, relating them to polygonal number-stuttered arithmetic progressions. The n-th element of the Connell sum sequence is established as a sharp upper bound for the value of a gamma-labeling of a graph of size n. The limiting behavior and a explicit formula for the Connell (m,r)-sum sequence are also given.
Friedel Craft's synthesis and characterization of some acene quinone compounds
Galleguillos, R.; Litt, M.; Rickert, S.E.
1987-01-01
The synthesis and characterization of some linear acene quinones of up to nine fused rings prepared by the Friedel-Craft's reaction of hydroquinone (HQ) and 1,4,9,10 tetrahydroxy anthracene (THA) with pyromellitic dianhydride (PMDA), and fused AlCl/sub 3/, was carried out. The intermediate product of the reaction of THA and PMDA, 1,4 dihydroxy anthraquinone, 6,7 dicarboxylic acid (DADCA) was also isolated and its synthesis optimized. This material was reduced to 1,4,9,10-tetrahydroxy anthracene 6,7-dicarboxylic acid (TADCA) and further dehydrated to its anhydride (TADCAmh). These compounds contain the necessary chemical functionalities which may lead to the facile synthesis of higher molecular weight quinones. These acene quinones show electronic spectral absorptions extending far into the NIR region, an indication of their long conjunction length.
Hydrogenative dearomatization of pyridine and an asymmetric aza-Friedel-Crafts alkylation sequence.
Wang, Shuo-Guo; You, Shu-Li
2014-02-17
Highly efficient synthesis of enantiomerically enriched substituted piperidines has been realized via chiral phosphoric acid catalyzed cascade hydrogenative dearomatization of substituted pyridines and aza-Friedel-Crafts reaction in good to excellent yields and enantioselectivity.
Deuteron dipole polarizabilities and sum rules
Friar, J.L.; Payne, G.L.
2005-07-01
The scalar, vector, and tensor components of the (generalized) deuteron electric dipole polarizability are calculated, as well as their logarithmic modifications. Several of these quantities arise in the treatment of the nuclear corrections to the deuterium Lamb shift and the deuterium hyperfine structure. A variety of second-generation potential models are used, and a (subjective) error is assigned to the calculations. The zero-range approximation is used to analyze a subset of the results, and a simple relativistic version of this approximation is developed.
Experimental study of isovector spin sum rules
Alexandre Deur; Peter Bosted; Volker Burkert; Donald Crabb; Kahanawita Dharmawardane; Gail Dodge; Tony Forest; Keith Griffioen; Sebastian Kuhn; Ralph Minehart; Yelena Prok
2008-02-04
We present the Bjorken integral extracted from Jefferson Lab experiment EG1b for $0.05<2.92$ GeV$^2$. The integral is fit to extract the twist-4 element $f_{2}^{p-n}$ which is large and negative. Systematic studies of this higher twist analysis establish its legitimacy at $Q^{2}$ around 1 GeV$^{2}$. We also extracted the isovector part of the generalized forward spin polarizability $\\gamma_{0}$. Although this quantity provides a robust test of Chiral Perturbation Theory, our data disagree with the calculations.
Ghahramany, N.; Khosravi, R.
2009-07-01
We investigate the rare semileptonic decays B{sub s}{yields}[f{sub 0}(980),K{sub 0}*(1430)]l{sup +}l{sup -}, (l=e, {mu}, {tau}), and B{sub s}{yields}[f{sub 0}(980),K{sub 0}*(1430)]{nu}{nu} in the framework of the three-point QCD sum rules. These decays are important to study because the f{sub 0}(980) and K{sub 0}*(1430) are the scalar mesons with total spin 0 and even parity and the quark content of them are still controversial in high energy physics. These rare decays occur at loop level by electroweak penguin and weak box diagrams in the standard model via the flavor changing neutral current transitions of b{yields}d, s, and not allowed by tree level. Considering the effective contributions of the nonperturbative parts of the correlation function, we calculate the relevant form factors of these transitions. The branching fractions and longitudinal lepton polarization asymmetry are also investigated.
Zhao, Xiaohu; Liu, Xiaohua; Mei, Hongjiang; Guo, Jing; Lin, Lili; Feng, Xiaoming
2015-03-23
A highly efficient asymmetric dearomatization of indoles was realized through a cascade reaction between 2-isocyanoethylindole and alkylidene malonates catalyzed by a chiral N,N'-dioxide/Mg(II) catalyst. Fused polycyclic indolines containing three stereocenters were afforded in good yields with excellent diastereo- and enantioselectivities through a Michael/Friedel-Crafts/Mannich cascade. When 2-substituted 2-isocyanoethylindoles were used, spiroindoline derivatives were obtained through a Michael/Friedel-Crafts reaction.
ERIC Educational Resources Information Center
Pong, Wai Yan
2007-01-01
We begin by answering the question, "Which natural numbers are sums of consecutive integers?" We then go on to explore the set of lengths (numbers of summands) in the decompositions of an integer as such sums.
ERIC Educational Resources Information Center
Pong, Wai Yan
2007-01-01
We begin by answering the question, "Which natural numbers are sums of consecutive integers?" We then go on to explore the set of lengths (numbers of summands) in the decompositions of an integer as such sums.
ERIC Educational Resources Information Center
Shi, Yixun
2010-01-01
Starting with an interesting number game sometimes used by school teachers to demonstrate the factorization of integers, "sum-difference numbers" are defined. A positive integer n is a "sum-difference number" if there exist positive integers "x, y, w, z" such that n = xy = wz and x ? y = w + z. This paper characterizes all sum-difference numbers…
ERIC Educational Resources Information Center
Shi, Yixun
2010-01-01
Starting with an interesting number game sometimes used by school teachers to demonstrate the factorization of integers, "sum-difference numbers" are defined. A positive integer n is a "sum-difference number" if there exist positive integers "x, y, w, z" such that n = xy = wz and x ? y = w + z. This paper characterizes all sum-difference numbers…
Hypercrosslinked polymeric foams prepared by Friedel-Crafts polycondensation
Steckle, W.P. Jr.; Mitchell, M.A.; Apen, P.G.
1996-10-01
Porous materials are widely used in industry and government for chemical separations, processing and monitoring, environmental cleanup and remediation, energy efficiency, and conservation. Porous materials used in these applications include: foams, filters, membranes, absorbents, ion exchange resins, molecular sieves, zeolites, catalyst supports, sensors, and electrodes. Organic analogues to inorganic zeolites would be a significant step forward in engineered porous materials and would provide advantages in range, selectivity, tailorability and processing. A novel process for preparing hypercrosslinked polymeric foams has been developed via a Friedel-Crafts polycondensation reaction. A series of rigid hypercrosslinked foams have been prepared using simple rigid polyaromatic hydrocarbons such as benzene, biphenyl, m-taphenyl, dipheny1methane, and polystyrene, with p-dichloroxylene as the crosslinking agent. After drying the gels, the resulting foams are robust and rigid. Their densities range from 0.3g/cc to 0.5g/cc. Nitrogen adsorption studies have shown that by judiciously selecting monomers and crosslinking agent along with the level of crosslinking, the pore size and distribution along with total surface area of the foam can be tailored. Surface areas range from 160 to 1,200 m{sup 2}/g with pore sizes ranging from 6{Angstrom} to 250{Angstrom}. Further evidence of this his been confirmed by high resolution TEM.
Hypercrosslinked polymeric foams prepared by Friedel-Crafts polycondensation
Steckle, W.P. Jr.; Mitchell, M.A.; Apen, P.G.
1995-12-31
Porous materials are widely used in industry and government for chemical separations, processing and monitoring, environmental cleanup and remediation, energy efficiency, and conservation. Porous materials used in these applications include: foams, filters, membranes, absorbents, ion exchange resins, molecular sieves, zeolites, catalyst supports, sensors, and electrodes. Organic analogues to inorganic zeolites would be a significant step forward in engineered porous materials and would provide advantages in range, selectivity, tailorability and processing. A novel process for preparing hypercross linked polymeric foams has been developed via a Friedel-Crafts polycondensation reaction. A series of rigid hypercrosslinked foams have been prepared using simple rigid polyaromatic hydrocarbons such as benzene, biphenyl, mterphenyl, diphenylmethane, and polystyrene, with p-dichloroxylene as the crosslinking agent. After drying the gels, the resulting foams are robust and rigid; densities range from 0.3 to 0.g/cc. Nitrogen adsorption studies have shown that by judiciously selecting monomers and crosslinking agent along with the level of crosslinking, the pore size and distribution along with total surface area of the foam can be tailored. Surface areas range from 160 to 1,200 m{sup 2}/g with pore sizes ranging from 6{Angstrom} to 250{Angstrom}. Further evidence of this has been confirmed by high resolution TEM.
Yang, Yan-Fang; Shu, Xing-Zhong; Wei, Hai-Long; Luo, Jian-Yi; Ali, Shaukat; Liu, Xue-Yuan; Liang, Yong-Min
2011-07-21
A useful method to construct highly substituted tetrahydroquinolines has been developed through an iron(III) chloride-mediated domino Mannich and intramolecular Friedel-Crafts alkylation followed by intermolecular Friedel-Crafts alkylation reactions of aliphatic aldehydes with aromatic amines.
NASA Astrophysics Data System (ADS)
Nath, N. M.; Das, M. K.; Sarma, J. K.
2016-01-01
A Q 2-dependent Regge ansatz for xF_3 (x,Q^2 ) structure function as the initial input is utilized to solve analytically the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equation in leading order, next-to-leading order and next-next-to-leading order. The solutions of the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi equations are also used to predict the Q 2 behavior of Gross-Llewellyn Smith sum rule. Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolved results for xF_3 (x,Q^2) structure functions as well as obtained sum rule results are analyzed phenomenologically in comparison with other results taken from Chicago-Columbia-Fermilab-Rochester, Neutrino experiment at the Fermlab Tevatron, CERN Hybrid Oscillation Research Apparatus and CERN-Dortmund-Heidelberg-Saclay-Warsaw collaborations, and a very good agreement is observed in this regard.
Aydin, C.; Yilmaz, A. H.; Bayar, M.
2010-05-01
We recalculated the coupling constants of {rho}({omega}){yields}{eta}{gamma} and {eta}{sup '{yields}{rho}}({omega}){gamma} decays especially with loop contributions in the case of axial-vector coupling in the method of QCD sum rules for dimension d=6. A comparison of our prediction on the coupling constants with the result obtained from analysis of the experimental data and calculations done before is performed.
Iron-catalyzed Friedel-Crafts benzylation with benzyl TMS ethers at room temperature.
Sawama, Yoshinari; Shishido, Yuko; Kawajiri, Takahiro; Goto, Ryota; Monguchi, Yasunari; Sajiki, Hironao
2014-01-07
Friedel-Crafts benzylations between unactivated arenes and benzyl alcohol derivatives are clean and straightforward processes to construct biologically useful di- and tri-arylmethanes. We have established an efficient iron-catalyzed Friedel-Crafts benzylation method at room temperature that uses benzyl TMS ethers as substrates, which are poorly reactive under common nucleophilic substitution conditions. The reaction seems to progress through iron-catalyzed self-condensation of the benzyl TMS ether to the corresponding dibenzylic ether. The use of excess arene relative to benzyl TMS ether produced mono-benzylated arene (di- and tri-arylmethane products), whereas the use of excess benzyl TMS ether versus arene provided bis-benzylated arene (polyarylated products) in high yields and regioselectivities. In previous methods, the latter double Friedel-Crafts benzylations hardly proceed.
Friedel-Crafts Coupling of Electron-Deficient Benzoylacetones Tuned by Remote Electronic Effects.
Luo, Hongmei; Pan, Ling; Xu, Xianxiu; Liu, Qun
2015-08-21
Acid-catalyzed electrophilic aromatic substitution for C-C bond formation, commonly referred to as the Friedel-Crafts reaction in recognition of its discoverers, has been one of the most useful reactions in organic chemistry for over a century. However, the Friedel-Crafts reaction cannot occur on a benzene ring having a strongly electron withdrawing group, such as an acyl group, which deactivates the aromatic ring toward electrophilic substitutions and remains a major challenge. Herein, the synthesis of naphthoquinones and 1,3-indandiones, bearing two acyl groups at positions ortho to each other on a benzene ring, are demonstrated by means of copper-catalyzed intramolecular aerobic oxidative acylation of benzoylacetone derivative precursors. This unusual Friedel-Crafts reaction reveals a new activation mode for the in situ polarity reverse of an electron-deficient aromatic ring to a reactive, electron-rich ring tuned by remote electronic effects.
Yamazaki, Shoko; Iwata, Yuko
2006-01-20
[reaction: see text] The Friedel-Crafts reaction is an important reaction for the formation of new C-C bonds. Recently, catalytic enantioselective Friedel-Crafts reaction of alkylidene malonates has been reported. However, the substituents in alkylidene malonates are limited. To explore new substituents such as carboxyl and carbonyl groups, catalytic enantioselective Friedel-Crafts reactions of reactive ethenetricarboxylates and acyl-substituted methylenemalonates 1 were investigated. The reaction of 1 with indoles in the presence of catalytic amounts of chiral bisoxazoline copper(II) complex (10%) in THF at room temperature gave alkylated products in high yields and up to 95% ee. The enantioselectivity can be explained by the secondary orbital interaction on approach of indole to the less hindered side of the 1-Cu(II)-ligand complex.
Wang, Y; Kong, C; Du, Y; Song, H; Zhang, D; Qin, Y
2012-04-14
Total syntheses of multidrug resistant inhibitors (-)-acetylardeemin 2a, (-)-ardeemin 2b, and (-)-formylardeemin 3 have been achieved within 10 steps starting from bromopyrroloinoline 13. The key step involves direct alkylation of 13 with prenyl tributylstannane 11 to yield 12 via a silver-promoted asymmetric Friedel-Crafts reaction. Highly efficient installation of the isoprenyl group allowed excellent overall yield. Moreover, the substrate scope of the asymmetric Friedel-Crafts reaction of 13 was expanded to include a variety of arenes 14 to afford natural product-like library analogues 15.
Dienamine and Friedel-Crafts one-pot synthesis, and antitumor evaluation of diheteroarylalkanals.
Frías, María; Padrón, José M; Alemán, José
2015-05-26
An asymmetric synthesis of diheteroarylalkanals through one-pot dienamine and Friedel-Crafts reaction is presented. The reaction tolerates a large variety of substituents at different positions of the starting aldehyde and also in the indole nucleophile, and a range of diheterocyclic alkanals can be achieved. Furthermore, we have studied the antiproliferative activity of these new compounds in representative cancer tumor cell lines.
Catalytic Asymmetric Synthesis of Chiral 2-Vinylindole Scaffolds by Friedel-Crafts Reaction.
Arai, Takayoshi; Tsuchida, Akiko; Miyazaki, Tomoya; Awata, Atsuko
2017-02-17
A chiral bis(imidazolidine)pyridine (PyBidine)-Ni(OTf)2 complex smoothly catalyzed an asymmetric Friedel-Crafts reaction of 2-vinylindoles with nitroalkenes to give chiral indoles in a highly enantioselective manner while maintaining the 2-vinyl functionality. The chiral 2-vinylindoles offer unique chiral scaffolds for diverse transformations.
Weng, Jian-Quan; Fan, Ren-Jie; Deng, Qiao-Man; Liu, Ren-Rong; Gao, Jian-Rong; Jia, Yi-Xia
2016-04-01
Highly enantioselective Friedel-Crafts C2-alkylation reactions of 3-substituted indoles with α,β-unsaturated esters and nitroalkenes were developed using chiral Lewis acids as catalysts, which afforded chiral indole derivatives bearing C2-benzylic stereogenic centers in good to excellent yields (up to 99%) and enantioselectivities (up to 96% ee).
Fang, Fang; Hua, Genghong; Shi, Feng; Li, Pengfei
2015-04-21
An organocatalytic asymmetric Friedel-Crafts reaction between indole and indole-derived hydroxylactams has been realized to furnish isoindolo-β-carbolines in good to excellent yields (up to >99%) and generally high enantioselectivities (up to >99% ee). The methodology offers an efficient access to functionalization of isoindolo-β-carbolines and preparation of chiral isoindolo-β-carboline derivatives.
Catalytic Friedel-Crafts Reactions of Highly Electronically Deactivated Benzylic Alcohols.
Vuković, Vuk D; Richmond, Edward; Wolf, Eléna; Moran, Joseph
2017-03-06
Highly electronically deactivated benzylic alcohols, including those with a CF3 group adjacent to the OH-bearing carbon, undergo dehydrative Friedel-Crafts reactions upon exposure to catalytic Brønsted acid in 1,1,1,3,3,3-hexafluoro-2-propanol (HFIP) solvent. Titration and kinetic experiments support the involvement of higher order solvent/acid clusters in catalysis.
Stereoselective double Friedel-Crafts alkylation of indoles with divinyl ketones.
Silvanus, Andrew C; Heffernan, Stephen J; Liptrot, David J; Kociok-Köhn, Gabriele; Andrews, Benjamin I; Carbery, David R
2009-03-05
A tandem double Friedel-Crafts reaction of indoles and nonsymmetrical divinyl ketones has been achieved. The tandem reaction forms complex [6-5-7]-tricyclic indoles in excellent yields. The reaction is completely regioselective and offers high levels of syn diastereoselectivity. The reaction is also seen to be sensitive to substrate structure and catalyst.
Friedel-Crafts Alkylation Using Elemental Aluminum Catalyst: An Undergraduate Laboratory Experiment.
ERIC Educational Resources Information Center
Meeks, B. Spencer; Lucas, Anita R.
1989-01-01
Provides methodology for carrying out the synthesis of sec-butyltoluene by the Friedel-Crafts alkylation of toluene. Suggests using simple elemental aluminum as the catalyst in place of AlCl3 or amalgamated aluminum. Notes satisfactory results for both macro- and microscale operations. (MVL)
Li, Chang-Feng; Liu, Hiu; Liao, Jie; Cao, Yi-Ju; Liu, Xiao-Peng; Xiao, Wen-Jing
2007-05-10
An enantioselective organocatalytic intramolecular ring-closing Friedel-Crafts-type alkylation of indolyl alpha,beta-unsaturated aldehydes has been developed. This powerful new strategy allows enantioselective access to THPIs and THBCs in a straightforward and atom-economical manner.
Enantioselective Friedel-Crafts alkylation for synthesis of 2-substituted indole derivatives.
Zhang, Yulong; Liu, Xiaohua; Zhao, Xiaohu; Zhang, Jianlin; Zhou, Lin; Lin, Lili; Feng, Xiaoming
2013-12-14
An efficient catalytic asymmetric intermolecular C2 Friedel-Crafts alkylation reaction between N-methyl skatole and β,γ-unsaturated α-ketoesters has been realized by a chiral N,N'-dioxide-Ni(II) complex. The corresponding indole derivatives were obtained in good yield (up to 96%) with excellent enantioselectivities (up to 99% ee) under mild reaction conditions.
Liu, Tian-Yu; Cui, Hai-Lei; Chai, Qian; Long, Jun; Li, Bang-Jing; Wu, Yong; Ding, Li-Sheng; Chen, Ying-Chun
2007-06-14
The asymmetric Michael-type Friedel-Crafts reaction of naphthols and nitroolefins promoted by bifunctional thiourea-tertiary amine organocatalysts (up to 95% ee) was investigated; on simply extending the reaction time further cascade reactions could occur to generate enantiopure dimeric tricyclic 1,2-dihydronaphtho[2,1-b]furanyl-2-hydroxylamine derivatives.
Friedel-Crafts Alkylation Using Elemental Aluminum Catalyst: An Undergraduate Laboratory Experiment.
ERIC Educational Resources Information Center
Meeks, B. Spencer; Lucas, Anita R.
1989-01-01
Provides methodology for carrying out the synthesis of sec-butyltoluene by the Friedel-Crafts alkylation of toluene. Suggests using simple elemental aluminum as the catalyst in place of AlCl3 or amalgamated aluminum. Notes satisfactory results for both macro- and microscale operations. (MVL)
1984-11-15
ag, o.. a RIM COMAS.,A, Organophosphazenes, 18 . Friedel-Crafts Technical Report Phenylation Reactions of Alkyl and Nimethylaming...Organophosphatenes. 18 . Frliedel-Crafts Phenylation Reactions of Alkyl and Dimethylauino Fluorocyclotriphoaphazenes Christopher Wf. Allen, Scott...intensities were .................. .... . - ..-...--. - . . * -..-....- °.- 6 corrected accordingly. The structure was solved by direct methods (MULTAN80) 18
Structure-property correlation study through sum-over-state approach
NASA Astrophysics Data System (ADS)
Nandi, P. K.; Hatua, K.; Bansh, A. K.; Panja, N.; Ghanty, T. K.
2015-01-01
The use of Thomas Kuhn (TK) sum rule in the expanded sum-over-state (SOS) expression of hyperpolarizabilities leads to various relationships between different order of polarizabilities and ground state dipole moment etc.
NASA Astrophysics Data System (ADS)
Granville, Andrew; Soundararajan, K.
2007-04-01
In 1918 Polya and Vinogradov gave an upper bound for the maximal size of character sums, which still remains the best known general estimate. One of the main results of this paper provides a substantial improvement of the Polya-Vinogradov bound for characters of odd, bounded order. In 1977 Montgomery and Vaughan showed how the Polya-Vinogradov inequality may be sharpened assuming the Generalized Riemann Hypothesis. We give a simple proof of their estimate and provide an improvement for characters of odd, bounded order. The paper also gives characterizations of the characters for which the maximal character sum is large, and it finds a hidden structure among these characters.
NASA Technical Reports Server (NTRS)
Robertson, G.
1982-01-01
Calibration was performed on the shuttle upper atmosphere mass spectrometer (SUMS). The results of the calibration and the as run test procedures are presented. The output data is described, and engineering data conversion factors, tables and curves, and calibration on instrument gauges are included. Static calibration results which include: instrument sensitive versus external pressure for N2 and O2, data from each scan of calibration, data plots from N2 and O2, and sensitivity of SUMS at inlet for N2 and O2, and ratios of 14/28 for nitrogen and 16/32 for oxygen are given.
Murashige, Ryo; Murai, Yuta; Hatanaka, Yasumaru; Hashimoto, Makoto
2009-06-01
The Friedel-Crafts reaction with 3-(3-methoxyphenyl)-3-(trifluoromethyl)-3H-diazirine and optically active N-TFA-Asp(Cl)-OMe in triflic acid afforded homophenylalanine derivatives without any loss of the optical purity.
Rueping, Magnus; Nachtsheim, Boris J
2010-01-20
The development of efficient Friedel-Crafts alkylations of arenes and heteroarenes using only catalytic amounts of a Lewis acid has gained much attention over the last decade. The new catalytic approaches described in this review are favoured over classical Friedel-Crafts conditions as benzyl-, propargyl- and allyl alcohols, or styrenes, can be used instead of toxic benzyl halides. Additionally, only low catalyst loadings are needed to provide a wide range of products. Following a short introduction about the origin and classical definition of the Friedel-Crafts reaction, the review will describe the different environmentally benign substrates which can be applied today as an approach towards greener processes. Additionally, the first diastereoselective and enantioselective Friedel-Crafts-type alkylations will be highlighted.
Wu, Kun; Zhuo, Ming-Hua; Sha, Di; Fan, Yan-Sen; An, Dong; Jiang, Yi-Jun; Zhang, Suoqin
2015-05-11
The first enantioselective aza-Friedel-Crafts reaction between pyrroles and enamides has been achieved by using a novel H8-BINOL-type imidodiphosphoric acid catalyst. This methodology was also applied to the highly enantioselective aza-Friedel-Crafts reaction between pyrroles and imines. The catalyst loadings in these two reactions are low (0.3-2 mol%). Both processes are amenable to gram scales.
Kim, Hun Young; Oh, Kyungsoo
2014-11-21
A one-pot synthesis of 2-naphthol derivatives is accomplished using a tandem Friedel-Crafts reaction sequence. The developed methodology allows for a concomitant construction of up to three C-C bonds between readily available alkynes and phenylacetyl chloride derivatives by an intermolecular Friedel-Crafts acylation of alkynes followed by an intramolecular Friedel-Crafts alkylation of β-chlorovinyl ketone intermediates.
Seo, Jeong-Min; Tan, Loon-Seng; Baek, Jong-Beom
2017-02-21
Popularly utilized oxidation media, via nitric acid/sulfuric acid mixtures, are too corrosive and oxidizing to preserve structural integrity of highly ordered graphitic materials (carbon nanotubes (CNTs) and graphene). Here, for the most commonly used oxidation method, the important advantages of defect/edge-selective functionalization of carbon materials (CNTs/graphene/graphite) in a polyphosphoric acid (PPA)/phosphorous pentoxide (P2 O5 ) medium are elucidated. The optimized PPA/P2 O5 medium is a mild acid that is not only less corrosive than popularly utilized oxidation media, but also has a strong capability to drive Friedel-Crafts acylation by covalently modifying carbon materials. With a broader spectrum of functional groups accessible, the PPA/P2 O5 -driven Friedel-Crafts acylation offers more options for tailoring the properties and processing of carbon materials.
NASA Astrophysics Data System (ADS)
Wang, Tao; Wu, An-an; Gao, Li-guo; Wang, Han-qing
2009-02-01
Electron paramagnetic resonance and electron-nuclear double resonance methods were used to study the polycyclic aromatic radical cations produced in a Friedel-Crafts alkylating system, with m-xylene, or p-xylene and alkyl chloride. The results indicate that the observed electron paramagnetic resonance spectra are due to polycyclic aromatic radicals formed from the parent hydrocarbons. It is suggested that benzyl halides produced in the Friedel-Crafts alkylation reactions undergo Scholl self-condensation to give polycyclic aromatic hydrocarbons, which are converted into corresponding polycyclic aromatic radical cations in the presence of AlCl3. The identification of observed two radicals 2,6-dimethylanthracene and 1,4,5,8-tetramethylanthracene were supported by density functional theory calculations using the B3LYP/6-31G(d,p)//B3LYP/6-31G(d) approach. The theoretical coupling constants support the experimental assignment of the observed radicals.
Nakamura, Shuichi; Matsuda, Nazumi; Ohara, Mutsuyo
2016-07-04
Organocatalytic enantioselective aza-Friedel-Crafts reactions of cyclic ketimines with pyrroles or indoles were catalyzed by imidazoline/phosphoric acid catalysts. The reaction was applied to various 3H-indol-3-ones to afford products in excellent yields and enantioselectivities. The chiral catalysts can be recovered by a single separation step using column chromatography and are reusable without further purification. Based on the experimental investigations, a possible transition state has been proposed to explain the origin of the asymmetric induction.
Griffiths, Kieran; Kumar, Prashant; Akien, Geoffrey R; Chilton, Nicholas F; Abdul-Sada, Alaa; Tizzard, Graham J; Coles, Simon J; Kostakis, George E
2016-06-14
A series of custom-designed, high yield, isoskeletal tetranuclear Zn/4f coordination clusters showing high efficiency as catalysts with low catalytic loadings in Friedel-Crafts alkylation are described for the first time. The possibility of altering the 4f centers in these catalysts without altering the core topology allows us to further confirm their stability via EPR and NMR, as well to gain insights into the plausible reaction mechanism, showcasing the usefulness of these bimetallic systems as catalysts.
Lewis Acid Catalyzed Friedel-Crafts Alkylation of Alkenes with Trifluoropyruvates.
Xiang, Bin; Xu, Teng-Fei; Wu, Liang; Liu, Ren-Rong; Gao, Jian-Rong; Jia, Yi-Xia
2016-05-06
A Friedel-Crafts alkylation reaction of styrenes with trifluoropyruvates has been developed, which delivered allylic alcohols in excellent yields (up to 98%) using the Ni(ClO4)2·6H2O/bipyridine complex as a catalyst. The asymmetric reaction was catalyzed by the chiral Cu(OTf)2/bisoxazoline complex to afford the corresponding chiral allylic alcohols bearing trifluoromethylated quaternary stereogenic centers in moderate enantioselectivities (up to 75% ee).
ZrCl4-mediated regio- and chemoselective Friedel-Crafts acylation of indole.
Guchhait, Sankar K; Kashyap, Maneesh; Kamble, Harshad
2011-06-03
An efficient method for regio- and chemoselective Friedel-Crafts acylation of indole using acyl chlorides in the presence of ZrCl(4) has been discovered. It minimizes/eliminates common competing reactions that occur due to high and multiatom-nucleophilic character of indole. In this method, a wide range of aroyl, heteroaroyl alkenoyl, and alkanoyl chlorides undergo smooth acylation with various indoles without NH protection and afford 3-acylindoles in good to high yields.
Counting Triangles to Sum Squares
ERIC Educational Resources Information Center
DeMaio, Joe
2012-01-01
Counting complete subgraphs of three vertices in complete graphs, yields combinatorial arguments for identities for sums of squares of integers, odd integers, even integers and sums of the triangular numbers.
ERIC Educational Resources Information Center
DeTemple, Duane
2010-01-01
Purely combinatorial proofs are given for the sum of squares formula, 1[superscript 2] + 2[superscript 2] + ... + n[superscript 2] = n(n + 1) (2n + 1) / 6, and the sum of sums of squares formula, 1[superscript 2] + (1[superscript 2] + 2[superscript 2]) + ... + (1[superscript 2] + 2[superscript 2] + ... + n[superscript 2]) = n(n + 1)[superscript 2]…
ERIC Educational Resources Information Center
DeTemple, Duane
2010-01-01
Purely combinatorial proofs are given for the sum of squares formula, 1[superscript 2] + 2[superscript 2] + ... + n[superscript 2] = n(n + 1) (2n + 1) / 6, and the sum of sums of squares formula, 1[superscript 2] + (1[superscript 2] + 2[superscript 2]) + ... + (1[superscript 2] + 2[superscript 2] + ... + n[superscript 2]) = n(n + 1)[superscript 2]…
Evaluation of lattice sums by the Poisson sum formula
NASA Technical Reports Server (NTRS)
Ray, R. D.
1975-01-01
The Poisson sum formula was applied to the problem of summing pairwise interactions between an observer molecule and a semi-infinite regular array of solid state molecules. The transformed sum is often much more rapidly convergent than the original sum, and forms a Fourier series in the solid surface coordinates. The method is applicable to a variety of solid state structures and functional forms of the pairwise potential. As an illustration of the method, the electric field above the (100) face of the CsCl structure is calculated and compared to earlier results obtained by direct summation.
Kumar, Akshay; Kaur, Jasneet; Chauhan, Pankaj; Chimni, Swapandeep Singh
2014-05-01
The Friedel-Crafts reaction of electron-rich phenols with isatins was developed by employing bifunctional thiourea-tertiary amine organocatalysts. Cinchona alkaloid derived thiourea epiCDT-3 a efficiently catalyzed the Friedel-Crafts-type addition of phenols to isatin derivatives to provide 3-aryl-3-hydroxy-2-oxindoles 7 and 9 in good yield (80-95 %) with good enantiomeric excess (83-94 %). Friedel-Crafts adduct 7 t was subjected to a copper(I)-catalyzed azide-alkyne cycloaddition to obtain biologically important 3-aryl-3-hydroxy-2-oxindole 11 in good enantiomeric excess and having a 1,2,3-triazole moiety.
Shirakawa, Eiji; Uchiyama, Nanase; Hayashi, Tamio
2011-01-07
FeCl(3) in combination with t-BuOOt-Bu as an oxidant was found to be an efficient catalyst for oxidation of alkylamides to α-(tert-butoxy)alkylamides. FeCl(2) and CuCl showed, respectively, almost the same and slightly lower activities compared with FeCl(3) in the tert-butoxylation of N-phenylpyrrolidone (1a), whereas no tert-butoxylated product was obtained by use of Fe(OTf)(3), RuCl(3), or Zr(OTf)(4). FeCl(3) was found to be effective also as a catalyst for the Friedel-Crafts alkylation with thus obtained α-(tert-butoxy)alkylamides. The Friedel-Crafts alkylation proceeded smoothly also in the presence of a catalytic amount of Fe(OTf)(3), RuCl(3), or Zr(OTf)(4). In contrast, FeCl(2) and CuCl, which showed certain activity toward the tert-butoxylation, failed to promote the Friedel-Crafts alkylation. Among the transition metal complexes thus far examined, only FeCl(3) showed high catalytic activities for both the oxidation and the Friedel-Crafts alkylation. The bifunctionality of FeCl(3) was utilized for the oxidative coupling of alkylamides with arenes through a tandem reaction consisting of oxidation of alkylamides to α-(tert-butoxy)alkylamides and the following Friedel-Crafts alkylation. The FeCl(3)-catalyzed oxidative coupling is applicable to a wide variety of alkylamides and arenes, though a combination of FeCl(3) with Fe(OTf)(3) was found to be effective for the reaction of arenes with low nucleophilicity. A Fe(II)-Fe(III) catalytic cycle is concerned with the tert-butoxylation, whereas a Fe(III) complex as a Lewis acid catalyzes the Friedel-Crafts alkylation.
Yoshida, Keisuke; Itatsu, Yukihiro; Fujino, Yuta; Inoue, Hiroki; Takao, Ken-Ichi
2016-06-01
The highly enantioselective organocatalytic construction of spiroindanes containing an all-carbon quaternary stereocenter by intramolecular Friedel-Crafts-type 1,4-addition is described. The reaction was catalyzed by a cinchonidine-based primary amine and accelerated by water and p-bromophenol. A variety of spiro compounds containing quaternary stereocenters were obtained with excellent enantioselectivity (up to 95 % ee). The reaction was applied to the asymmetric formal synthesis of the spirocyclic natural products (-)-cannabispirenones A and B.
Wang, Xin-Wei; Hua, Yuan-Zhao; Wang, Min-Can
2016-10-07
A direct asymmetric Friedel-Crafts (F-C) alkylation reaction between a wide range of indoles and ethyl 2-(4-methoxyphenylimino)acetate catalyzed by Trost's dinuclear complex is reported. A series of 3-indolylglycine derivatives were synthesized in enantioselectivity of up to >99% enantiomeric excess (ee) using 10 mol% catalyst loading under mild conditions. This atom economic reaction could be run on a gram scale without impacting its enantioselectivity. The absolute stereochemistry of catalytic products was determined by correlation with a known configuration compound. A possible mechanism was proposed for the asymmetric induction.
Ren, Hai; Wang, Pan; Wang, Lijia; Tang, Yong
2015-10-02
A highly enantioselective and regioselective chiral Lewis acid catalyzed tandem Friedel-Crafts/lactonization reaction is reported, providing direct access to plenty of 3-hydroxy-3-trifluoromethyl benzofuran-2-ones in up to 94% yields with up to >99% ee. Mechanistic study reveals that the interactions between the phenolic hydroxyl group and trifluoropyruvate are the most likely contributing factor to the high enantio- and regioselectivity. Optically pure (-)-BHFF can be obtained in gram-scale with 0.05 mol % catalyst, demonstrating the potentially utility of this method in medicinal chemistry.
Pallikonda, Gangaram; Chakravartya, Manab
2016-03-04
Easily reachable electron-poor/rich primary and secondary benzylic phosphates are suitably used as substrates for Friedel-Crafts benzylation reactions with only 1.2 equiv activated/deactivated arenes (no additional solvent) to access structurally and electronically diverse polyarylated alkanes with excellent yields and selectivities at room temperature. Specifically, diversely substituted di/triarylmethanes are generated within 2-30 min using this approach. A wide number of electron-poor polyarylated alkanes are easily accomplished through this route by just tuning the phosphates.
Catalytic Selenium-Promoted Intermolecular Friedel-Crafts Alkylation with Simple Alkenes.
Tang, E; Zhao, Yinjiao; Li, Wen; Wang, Weilin; Zhang, Meng; Dai, Xin
2016-03-04
A method for conducting selenium-promoted intermolecular Friedel-Crafts (F-C) alkylation reactions has been developed with simple alkenes using trimethylsilyl trifluoromethanesulfonate as a catalyst and N-phenylselenophthalimide as an efficient selenium source. Electron-rich arenes smoothly underwent F-C alkylation with a variety of alkenes to afford alkylated products in good yield and with high regioselectivity and diastereoselectivity. The regioselectivity and stereoselectivity of arenes and alkenes as well as a preliminary mechanism of the F-C alkylation reaction are discussed.
NASA Astrophysics Data System (ADS)
Maltsev, O. V.; Beletskaya, Irina P.; Zlotin, Sergei G.
2011-11-01
Recent applications of organocatalytic Michael and Friedel-Crafts reactions in enantioselective synthesis of biologically active compounds: natural products, pharmaceutical agents and plant protection agents are reviewed. The key mechanisms of stereoinduction, types of organocatalysts and reagents used in these reactions are considered. The material is classified according to the type of newly formed bonds incorporating the asymmetric carbon atom, and the information for the most numerous C-C coupling reactions is systematized according to the natures of the electrophile and the nucleophile. The bibliography includes 433 references. Dedicated to Academician O M Nefedov on the occasion of his 80th birthday.
Remote enantioselective Friedel-Crafts alkylations of furans through HOMO activation.
Li, Jun-Long; Yue, Cai-Zhen; Chen, Peng-Qiao; Xiao, You-Cai; Chen, Ying-Chun
2014-05-19
Catalytic asymmetric Friedel-Crafts alkylation is a powerful protocol for constructing a chiral C(sp(2))-C(sp(3)) bond. Most previous examples rely on LUMO activation of the electrophiles using chiral catalysts with subsequent attack by electron-rich arenes. Presented herein is an alternative strategy in which the HOMO of the aromatic π system of 2-furfuryl ketones is raised through the formation of a formal trienamine species using a chiral primary amine. Exclusive regioselective alkylation at the 5-position occurred with alkylidenemalononitriles, and high reactivity and excellent enantioselectivity (up to 95% ee) was obtained by this remote activation.
Shirinian, Valerii Z; Lvov, Andrey G; Yadykov, Anton V; Yaminova, Liana V; Kachala, Vadim V; Markosyan, Ashot I
2016-12-16
The acid-catalyzed cyclization of a wide range of triaryl-substituted divinyl ketones has been studied. It was found that the reaction pathway strongly depends on the nature of the aryl substituent at the α-position to the carbonyl group. An electron-rich aromatic substituent promotes the reaction to proceed through the intramolecular Friedel-Crafts electrophilic substitution giving dihydronaphthalene derivatives. In contrast, the presence of an electron-deficient substituent is favorable for the Nazarov 4π-conrotatory cyclization yielding triaryl-substituted cyclopentenones. The electrophilic substitution reaction was applied to thiophene and thiazole derivatives.
Huang, Zhiliang; Jin, Liqun; Han, Heyou; Lei, Aiwen
2013-03-21
AlCl(3) promoted Friedel-Crafts acylation between 4-tert-butylbenzoyl chloride and mesitylene was investigated. The donor-acceptor complex was observed as the major species. Kinetic investigation demonstrated that the reaction was first-order on the donor-acceptor complex and zero-order on ArH, suggesting that the donor-acceptor complex was not the true reactive species. However, the acylium ion was almost invisible with a fairly low concentration under live reaction conditions. It was approved as the true reactive species through kinetic data ("kinetic capture") in the AlCl(3) promoted Friedel-Crafts acylation reaction.
Probability density functions of the average and difference intensities of Friedel opposites.
Shmueli, U; Flack, H D
2010-11-01
Trigonometric series for the average (A) and difference (D) intensities of Friedel opposites were carefully rederived and were normalized to minimize their dependence on sin(theta)/lambda. Probability density functions (hereafter p.d.f.s) of these series were then derived by the Fourier method [Shmueli, Weiss, Kiefer & Wilson (1984). Acta Cryst. A40, 651-660] and their expressions, which admit any chemical composition of the unit-cell contents, were obtained for the space group P1. Histograms of A and D were then calculated for an assumed random-structure model and for 3135 Friedel pairs of a published solved crystal structure, and were compared with the p.d.f.s after the latter were scaled up to the histograms. Good agreement was obtained for the random-structure model and a qualitative one for the published solved structure. The results indicate that the residual discrepancy is mainly due to the presumed statistical independence of the p.d.f.'s characteristic function on the contributions of the interatomic vectors.
NIS-assisted aza-Friedel-Crafts reaction with α-carbamoysulfides as precursors of N-carbamoylimines.
George, Nicolas; Bekkaye, Mathieu; Alix, Aurélien; Zhu, Jieping; Masson, Géraldine
2014-03-24
A general and practical N-iodosuccinimide (NIS)-promoted aza-Friedel-Crafts reaction of various aromatic nucleophiles with N-acylimines generated in situ from α-amidosulfides to give a rapid access to highly functionalized amines is described. The newly developed methodology is very mild, fast, efficient, and complementary.
Zhao, Zheng-Le; Xu, Qing-Long; Gu, Qing; Wu, Xin-Yan; You, Shu-Li
2015-03-14
Palladium-catalyzed asymmetric intramolecular Friedel-Crafts type allylic alkylation reaction of phenols was developed under mild conditions. In the presence of Pd2(dba)3 with (1R,2R)-DACH-phenyl Trost ligand (L2) in toluene at 50 °C, the reaction provides various C4 substituted tetrahydroisoquinolines with moderate to excellent yields, regioselectivity and enantioselectivity.
Intramolecular Friedel-Crafts Acylation Reaction Promoted by 1,1,1,3,3,3-Hexafluoro-2-propanol.
Motiwala, Hashim F; Vekariya, Rakesh H; Aubé, Jeffrey
2015-11-06
Simple dissolution of an arylalkyl acid chloride in 1,1,1,3,3,3-hexafluoro-2-propanol promotes an intramolecular Friedel-Crafts acylation without additional catalysts or reagents. This reaction is operationally trivial in both execution and product isolation (only requiring concentration followed by purification) and accommodates a broad range of substrates. Preliminary studies that bear upon potential reaction mechanisms are reported.
Philipps, Arne R; Fritze, Lars; Erdmann, Nico; Enders, Dieter
2015-04-02
An organocatalytic quadruple cascade initiated by a Friedel-Crafts-type reaction is described. The (S)-diphenylprolinol trimethylsilyl ether catalyzed reaction yields highly functionalized cyclohexenecarbaldehydes bearing a 1,1-bis[4-(dialkylamino)phenyl]ethene moiety and three contiguous stereogenic centers. The reaction tolerates various functional groups and all products are obtained with very good diastereoselectivity and with virtually complete enantiomeric excess.
Ge, Chen; Liu, Ren-Rong; Gao, Jian-Rong; Jia, Yi-Xia
2016-07-01
A highly enantioselective Friedel-Crafts alkylation of indoles with N-sulfonylaziridines as alkylating agents has been developed by utilizing the complex of Cu(CH3CN)4BF4/(S)-Segphos as a catalyst. A range of optically active tryptamine derivatives are obtained in good to excellent yields and enantioselectivities (up to >99% ee) via a kinetic resolution process.
Yang, Guang-Jun; Du, Wei; Chen, Ying-Chun
2016-10-21
An asymmetric Friedel-Crafts alkylation reaction of 2-furfuryl ketones with β-trifluoromethyl enones has been developed via formal trienamine catalysis of a bifunctional primary amine-thiourea substance derived from L-tert-leucine, delivering the furan derivatives incorporating a stereogenic trifluoromethyl (CF3) group in good to high yields with excellent enantioselectivity.
Akbar, Sikkandarkani; Srinivasan, Kannupal
2016-02-05
o-Alkynyldihydrochalcones when treated with a catalytic amount of anhydrous FeCl3 in refluxing 1,2-dichloroethane underwent tandem Conia-ene and Friedel-Crafts reactions to yield benzo[b]fluorene derivatives in good yields.
Peng, Jiahuan; Du, Da-Ming
2013-01-01
The enantioselective tandem Friedel-Crafts alkylation/Michael addition reaction of indoles with nitroolefin enoates catalyzed by a diphenylamine-linked bis(oxazoline)-Zn(OTf)2 complex was investigated. This tandem reaction afforded functionalized chiral chromans in good yields with moderate to high stereoselectivities (up to 95:5 dr, up to 99% ee).
Valset, K; Tafto, J
2011-06-01
We classify the point symmetries at the different points in the Brillouin zone for the 17 two-dimensional space groups and the symmetries of the Bloch waves for the 10 two-dimensional crystallographic point groups. Simple examples involving breakdown of Friedels law, Gjonnes-Moodie lines, and reflection and refraction at interfaces are presented.
Ishikawa, Teruhiko; Manabe, Shinobu; Aikawa, Toshiaki; Kudo, Takayuki; Saito, Seiki
2004-07-08
[reaction: see text] This paper describes a novel method to synthesize a quinoline backbone by incorporating allenyl cations into a catalytic intramolecular Friedel-Crafts reaction. The initial products were isomerized and aromatized upon treatment with acid and base, respectively, to give quinolines. The basic concept also proved to be promising for 1-benzazepine, 1-benzazocine, or isoquinoline synthesis.
Wang, Wentao; Lian, Xiangjin; Chen, Donghui; Liu, Xiaohua; Lin, Lili; Feng, Xiaoming
2011-07-21
An efficient yttrium(III)-catalyzed highly enantioselective Friedel-Crafts alkylation of β-trichloro(trifluoro)methyl aryl enones is described. The reaction delivered a series of functionalized indoles with a chiral tertiary carbon center bearing a trichloro(trifluoro)methyl group in excellent results (up to 96% ee and 99% yield) under mild conditions.
Zhou, Si-Li; Li, Jun-Long; Dong, Lin; Chen, Ying-Chun
2011-11-04
A highly enantioselective aza-Diels-Alder and Friedel-Crafts reaction sequence of N-sulfonyl-1-aza-1,3-butadienes and aliphatic aldehydes tethered to an arene motif has been developed, affording the fused chiral piperidine frameworks with a versatile scaffold diversity. A similar strategy has been applied for the construction of complex chiral tetrahydroquinoxaline structures.
Hui, Yonghai; Zhang, Qi; Jiang, Jun; Lin, Lili; Liu, Xiaohua; Feng, Xiaoming
2009-09-04
An efficient enantioselective Friedel-Crafts alkylation of indoles to ethyl glyoxylate catalyzed by chiral N,N'-dioxide-Sc(III) complex was developed. The corresponding 3-indolyl(hydroxy)acetates compounds were afforded in good yields with high enantioselectivities (up to 95% ee).
Li, Guo-Xing; Qu, Jin
2012-06-04
Enantioselective Friedel-Crafts reactions between phenols and N-tosylaldimines were developed using a bifunctional catalyst readily prepared from L-leucine. The chiral benzylic amine products were obtained in high yields (up to 96% yield) and good to high enantiomeric excesses (up to 95% ee).
NASA Astrophysics Data System (ADS)
Desgranges, Caroline; Huber, Landon; Delhommelle, Jerome
2016-07-01
We determine the impact of the Friedel oscillations on the phase behavior, critical properties, and thermodynamic contours in films [two dimensions (2 D )] and bulk phases [three dimensions (3 D )]. Using expanded Wang-Landau simulations, we calculate the grand-canonical partition function and, in turn, the thermodynamic properties of systems modeled with a linear combination of the Lennard-Jones and Dzugutov potentials, weighted by a parameter X (0
Croft, Rosemary A; Mousseau, James J; Choi, Chulho; Bull, James A
2016-11-02
The first examples of 3,3-diaryloxetanes are prepared in a lithium-catalyzed and substrate dependent divergent Friedel-Crafts reaction. para-Selective Friedel-Crafts reactions of phenols using oxetan-3-ols afford 3,3-diaryloxetanes by displacement of the hydroxy group. These constitute new isosteres for benzophenones and diarylmethanes. Conversely, ortho-selective Friedel-Crafts reactions of phenols afford 3-aryl-3-hydroxymethyl-dihydrobenzofurans by tandem alkylation-ring-opening reactions; the outcome of the reaction diverging to structurally distinct products dependent on the substrate regioselectivity. Further reactivity of the oxetane products is demonstrated, suitable for incorporation into drug discovery efforts.
Friedel's salt formation in sulfoaluminate cements: A combined XRD and {sup 27}Al MAS NMR study
Paul, G.; Boccaleri, E.; Buzzi, L.; Canonico, F.; Gastaldi, D.
2015-01-15
Four different binders based on calcium sulfoaluminate cements have been submitted to accelerated chlorination through ionic exchange on hydrated pastes, in order to investigate their ability to chemically bind chloride ions that might reduce chloride penetration. The composition of hydrated cements before and after the treatment was evaluated by means of an X-Ray Diffraction–{sup 27}Al Magic Angle Spinning Nuclear Magnetic Resonance Spectroscopy combined study, allowing to take into account even partially amorphous phases and to make quantitative assumption on the relative abundance of the different aluminium-containing phases. It was found that low SO{sub 3} Sulfoaluminate–Portland ternary systems are the most effective in binding chloride ions and the active role played by different members of the AFm family in chloride uptake was confirmed. Moreover, a peculiar behavior related to the formation of Friedel's salt in different pH conditions was also established for the different cements.
Pecchioli, Tommaso; Muthyala, Manoj Kumar; Haag, Rainer; Christmann, Mathias
2015-01-01
The first immobilization of a MacMillan's first generation organocatalyst onto dendritic support is described. A modified tyrosine-based imidazolidin-4-one was grafted to a soluble high-loading hyperbranched polyglycerol via a copper-catalyzed alkyne-azide cycloaddition (CuAAC) reaction and readily purified by dialysis. The efficiency of differently functionalized multivalent organocatalysts 4a-c was tested in the asymmetric Friedel-Crafts alkylation of N-methylpyrrole with α,β-unsaturated aldehydes. A variety of substituted enals was investigated to explore the activity of the catalytic system which was also compared with monovalent analogues. The catalyst 4b showed excellent turnover rates and no loss of activity due to immobilization, albeit moderate enantioselectivities were observed. Moreover, easy recovery by selective precipitation allowed the reuse of the catalyst for three cycles.
Strong Quantum Size Effects in Pb(111) Thin Films Mediated by Anomalous Friedel Oscillations
Jia, Yu; Wu, Biao; Li, Chong; Eguiluz, Adolfo G; Weitering, Hanno; Zhang, Zhenyu
2010-01-01
Using first-principles calculations within density functional theory, we study Friedel oscillations (FOs) in the electron density at different metal surfaces and their influence on the lattice relaxation and stability of ultrathin metal films.We show that the FOs at the Pb(111) surface decay as 1=x with the distance x from the surface, different from the conventional 1=x2 power law at other metal surfaces. The underlying physical reason for this striking difference is tied to the strong nesting of the two different Fermi sheets along the Pb(111) direction. The interference of the strong FOs emanating from the two surfaces of a Pb(111) film, in turn, not only results in superoscillatory interlayer relaxations around the center of the film, but also determines its stability in the quantum regime. As a simple and generic picture, the present findings also explain why quantum size effects are exceptionally robust in Pb(111) films.
Friedel oscillations in graphene-based systems probed by Scanning Tunneling Microscopy
NASA Astrophysics Data System (ADS)
Mallet, Pierre; Brihuega, Iván; Cherkez, Vladimir; Gómez-Rodríguez, Jose Marìa; Veuillen, Jean-Yves
2016-03-01
For the last 25 years, scientists have demonstrated the capabilities of Scanning Tunneling Microscopy (STM) to visualize in real space the response of a two-dimensional electron gas to atomic-scale impurities. The analysis of the Friedel oscillations surrounding the impurities yields valuable information regarding the elastic scattering properties, the band structure, the doping level and the symmetry of the electronic states in the two-dimensional host system. We will address in this article the use of this technique for probing the electronic properties of graphene, the star two-dimensional compound of the last decade. In particular, we will emphasize how this technique can be pushed up to unravel the electronic pseudospin, a distinctive degree of freedom of graphene's Dirac fermions.
Environmentally benign Friedel-Crafts benzylation over nano-TiO2/SO4 2-
NASA Astrophysics Data System (ADS)
Devi, Kalathiparambil RPS; Sreeja, Puthenveetil B.; Sugunan, Sankaran
2013-05-01
During the past decade, much attention has been paid to the replacement of homogeneous catalysts by solid acid catalysts. Friedel-Crafts benzylation of toluene with benzyl chloride (BC) in liquid phase was carried out over highly active, nano-crystalline sulfated titania systems. These catalysts were prepared using the sol gel method. Modification was done by loading 3% of transition metal oxides over sulfated titania. Reaction parameters such as catalyst mass, molar ratio, temperature, and time have been studied. More than 80% conversion of benzyl chloride and 100% selectivity are shown by all the catalysts under optimum conditions. Catalytic activity is correlated with Lewis acidity obtained from perylene adsorption studies. The reaction appears to proceed by an electrophile, which involves the reaction of BC with the acidic titania catalyst. The catalyst was regenerated and reused up to four reaction cycles with equal efficiency as in the first run. The prepared systems are environmentally friendly and are easy to handle.
Small sum privacy and large sum utility in data publishing.
Fu, Ada Wai-Chee; Wang, Ke; Wong, Raymond Chi-Wing; Wang, Jia; Jiang, Minhao
2014-08-01
While the study of privacy preserving data publishing has drawn a lot of interest, some recent work has shown that existing mechanisms do not limit all inferences about individuals. This paper is a positive note in response to this finding. We point out that not all inference attacks should be countered, in contrast to all existing works known to us, and based on this we propose a model called SPLU. This model protects sensitive information, by which we refer to answers for aggregate queries with small sums, while queries with large sums are answered with higher accuracy. Using SPLU, we introduce a sanitization algorithm to protect data while maintaining high data utility for queries with large sums. Empirical results show that our method behaves as desired. Copyright © 2014 Elsevier Inc. All rights reserved.
Guo, Ying-Cen; Li, Dong-Ping; Li, Yu-Ling; Wang, Hong-Mei; Xiao, Wen-Jing
2009-08-01
Organocatalytic enantioselective synthesis of alpha-indolyl phosphonates has been successfully carried out via asymmetric Friedel-Crafts alkylation of substituted indoles with (E)-dialkyl 3-oxoprop-1-enylphosphonates in 48-82% yield and 73-96% ee.
Three nucleon forces in nuclear matter in QCD sum rules
NASA Astrophysics Data System (ADS)
Drukarev, E. G.; Ryskin, M. G.; Sadovnikova, V. A.
2017-03-01
We calculate the single-particle nucleon characteristics in symmetric nuclear matter with inclusion of the 3N interactions. The contributions of the 3N forces to nucleon self energies are expressed in terms of the nonlocal scalar condensate (d = 3) and of the configuration of the four-quark condensates (d = 6) in which two diquark operators act on two different nucleons of the matter. The most important part of the contribution of the four-quark condensate is calculated in a model-independent way. We employed a relativistic quark model of nucleon for calculation of the other parts. The density dependence of the vector and scalar nucleon self energies and of the single-particle potential energy are obtained. Estimations on contributions of the 4N forces to the nucleon self energies are made.
Energy-weighted sum rules, y-scaling and duality
J. Wallace Van Orden; Sabine Jeschonnek
2002-09-01
The phenomena of scaling and Bloom-Gilman duality are examined in the context of simple nonrelativistic and relativistic quantum mechanical models. These models are shown to scale and to show the qualitative feature of Bloom-Gilman duality. This suggests that these phenomena do not necessarily require the properties of QCD.
On the dipole polarisability and dipole sum rules of ozone
NASA Astrophysics Data System (ADS)
Kalugina, Yulia N.; Thakkar, Ajit J.
2015-10-01
Ab initio calculations of the dipole polarisability and other Cauchy moments of the dipole oscillator strength distribution (DOSD) of ozone are reported to help resolve discrepancies between theory and experiment. A number of coupled-cluster methods based on a Hartree-Fock reference function, multiconfiguration-reference configuration interaction methods, and perturbatively corrected, complete-active-space self-consistent field methods are used. The C DOSD of Kumar and Thakkar is probably preferable to their B1 distribution. Our best estimate of the mean polarisability is ? atomic units.
Sum Rules for Optical Extinction and Scattering by Small Particles.
1986-03-18
and some areas of optics, particularly optical properties of solids (e.g., Stern, 1963), they have been largely ignored by workers in the field of...Elementary theory of the optical properties of solids . Sold State Phys. 15, 299-408. A , a. - . - . A - - .4 4 ) J N
Wang, Yingcheng; Jiang, Liang; Li, Long; Dai, Jun; Xiong, Dan; Shao, Zhihui
2016-11-21
The first arylation strategy for the synthesis of enantioenriched propargylamines is disclosed. This approach, which is complementary to previous alkynylation and alkylation strategies, involves a C(sp(2) )-C(sp(3) ) bond formation, and is based on the first asymmetric Friedel-Crafts-type arylation reaction of C-alkynyl imines. Asymmetric Friedel-Crafts reactions with electron-deficient phenols, a longstanding unsolved challenge, have thus been realized for the first time, enabled by the combination of our recently introduced C-alkynyl N-Boc-protected N,O-acetals as electrophiles and chiral phosphoric acids as catalysts. The synthetic utility of the resulting structurally diverse and polyfunctional chiral propargylamines was demonstrated by a series of selective transformations, including controlled reduction of the alkynyl group and iterative cross-couplings.
Direct Sum Decomposition of Groups
ERIC Educational Resources Information Center
Thaheem, A. B.
2005-01-01
Direct sum decomposition of Abelian groups appears in almost all textbooks on algebra for undergraduate students. This concept plays an important role in group theory. One simple example of this decomposition is obtained by using the kernel and range of a projection map on an Abelian group. The aim in this pedagogical note is to establish a direct…
Direct Sum Decomposition of Groups
ERIC Educational Resources Information Center
Thaheem, A. B.
2005-01-01
Direct sum decomposition of Abelian groups appears in almost all textbooks on algebra for undergraduate students. This concept plays an important role in group theory. One simple example of this decomposition is obtained by using the kernel and range of a projection map on an Abelian group. The aim in this pedagogical note is to establish a direct…
ERIC Educational Resources Information Center
Fay, Temple H.
1997-01-01
Presents an exercise suitable for beginning calculus students that may give insight into series representations and allow students to see some elementary application of these representations. The Fourier series is used to approximate by taking sums of trigonometric functions of the form sin(ns) and cos(nx) for n is greater than or = zero. (PVD)
Champagne, Pier Alexandre; Benhassine, Yasmine; Desroches, Justine; Paquin, Jean-François
2014-12-08
A Friedel-Crafts benzylation of arenes with benzyl fluorides has been developed. The reaction produces 1,1-diaryl alkanes in good yield under mild conditions without the need for a transition metal or a strong Lewis acid. A mechanism involving activation of the C-F bond through hydrogen bonding is proposed. This mode of activation enables the selective reaction of benzylic C-F bonds in the presence of other benzylic leaving groups.
Qiao, Shuo; Mo, Junming; Wilcox, Cody B; Jiang, Bo; Li, Guigen
2017-02-21
The design and synthesis of recyclable imidazolidinone catalysts using GAP chemistry/technique was described. Their applications in asymmetric Diels-Alder and Friedel-Crafts reactions with α,β-unsaturated aldehydes resulted in excellent yields and higher enantioselectivities than previous processes. As recyclable small molecular catalysts, phosphonylated imidazolidinones can be recovered and reused for up to three runs without costing significant decrease in catalytic activity.
Beaud, Rodolphe; Guillot, Régis; Kouklovsky, Cyrille; Vincent, Guillaume
2012-12-07
IRONic electrophilic indoles! The C3-regioselective hydroarylation of N-acetyl indoles with aromatic nucleophiles mediated by FeCl(3) features a rare example of the electrophilic reactivity of the indole core in a Friedel-Crafts reaction. This indole umpolung allows us straightforward access to the tetracyclic benzofuroindoline motif found in the natural product diazonamide A, which is a potent antitumor agent. Copyright © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Bai, Sha; Liao, Yuting; Lin, Lili; Luo, Weiwei; Liu, Xiaohua; Feng, Xiaoming
2014-11-07
A highly efficient aza-Friedel-Crafts reaction of sesamol with aldimines has been realized by using a chiral N,N'-dioxide-scandium(III) complex as the catalyst. A series of corresponding bioactive chiral α-amino-sesamols were obtained in moderate to good yields (up to 97%) with excellent enantioselectivities (up to 97% ee). Furthermore, the control experiments were conducted to provide fundamental insights into the mechanism of the reaction.
Dhiman, Seema; Ramasastry, S S V
2013-12-14
An efficient synthetic approach to diheteroarylmethanes and 1,3-diheteroarylpropenes has been developed via Yb(III)-catalyzed sequential self-condensation of 2-furfuryl (or 2-thienyl or 3-indolyl) alcohols followed by intramolecular Friedel-Crafts type reaction and elimination of an aldehyde. This method offers a powerful entry and a potential alternative to the traditional synthesis of diheteroarylalkanes, which are precursors to the synthesis of several intriguing heteroaryls and more significantly, to the synthesis of biofuels.
Summing Planar Bosonic Open Strings
Bardakci, Korkut
2006-02-16
In earlier work, planar graphs of massless {phi}{sup 3} theory were summed with the help of the light cone world sheet picture and the mean field approximation. In the present article, the same methods are applied to the problem of summing planar bosonic open strings. They find that in the ground state of the system, string boundaries form a condensate on the world sheet, and a new string emerges from this summation. Its slope is always greater than the initial slope, and it remains non-zero even when the initial slope is set equal to zero. If they assume the initial string tends to a field a theory in the zero slope limit, this result provides evidence for string formation in field theory.
Torque-Summing Brushless Motor
NASA Technical Reports Server (NTRS)
Vaidya, J. G.
1986-01-01
Torque channels function cooperatively but electrically independent for reliability. Brushless, electronically-commutated dc motor sums electromagnetic torques on four channels and applies them to single shaft. Motor operates with any combination of channels and continues if one or more of channels fail electrically. Motor employs single stator and rotor and mechanically simple; however, each of channels electrically isolated from other so that failure of one does not adversely affect others.
A novel mesoporous sulfated zirconium solid acid catalyst for Friedel-Crafts benzylation reaction
NASA Astrophysics Data System (ADS)
Miao, Zhichao; Zhou, Jin; Zhao, Jinping; Liu, Dandan; Bi, Xu; Chou, Lingjun; Zhuo, Shuping
2017-07-01
In this paper, a novel mesoporous sulfated zirconium (M-ZrO2/SO42-) has been gotten by one-pot evaporation-induced self-assembly (one-pot EISA) strategy. The SXRD, N2-physisorption and TEM characterization techniques indicated that M-ZrO2/SO42- possessed distinct mesostructure with big specific surface area (133.5 m2 g-1), large pore volume (0.18 cm3 g-1) and narrow pore size distribution (4.90 nm). Moreover, the existing states and the influence in mesostructure of introduced S species were detailedly investigated by the XRD, N2-physisorption, TEM, TG-DSC, FT-IR and XPS techniques and the results showed that the S species, which existed as the type of SO42-, improved the textural properties of prepared materials. In addition, the NH3-TPD and IR spectra of adsorbed pyridine indicated the existence of strong Brønsted and Lewis acid sites in M-ZrO2/SO42- even evacuated at 400 °C. Furthermore, the M-ZrO2/SO42- was used as a promise solid acid catalyst and displayed excellent catalytic performance and reusability in Friedel-Crafts benzylation reaction.
Test kit/spectrometer for the analysis of petroleum substances using Friedel-Crafts colorimetry
NASA Astrophysics Data System (ADS)
Hanby, John D.; Hewitt, Alan D.; Lory, Ernest E.
2001-02-01
12 Laboratory and field results of the testing of a new, visible-range spectrometry utilizing the robust signals produced by Friedel-Crafts reaction compounds demonstrate the utility of a rapid, portable, and sensitive method of on-site analysis for petroleum substances in soil and water samples. Preliminary testing of the kits and spectrometer was performed at the U.S. Army Cold Regions Research and Engineering Laboratory (CRREL) in Hanover, NH. Specific field protocols for the sampling and handling of soils for gasoline range organics and diesel range organics were established for the field sampling, which was conducted at the U.S. Navy Facilities Engineering Service Center in Port Hueneme, CA. Co-located soil samples were collected and either split or homogenized for subsequent partitioning to provide samples for the on-site analysis by the field kit/spectrometer technology and for later analysis by off- site reference laboratories. Test kit colorimetric results are by visual and spectrometric methods, and are compared with reference laboratory results and CRREL analyses.
Anisotropic density fluctuations, plasmons, and Friedel oscillations in nodal line semimetal
NASA Astrophysics Data System (ADS)
Rhim, Jun-Won; Kim, Yong Baek
2016-04-01
Motivated by recent experimental efforts on three-dimensional semimetals, we investigate the static and dynamic density response of the nodal line semimetal by computing the polarizability for both undoped and doped cases. The nodal line semimetal in the absence of doping is characterized by a ring-shape zero energy contour in momentum space, which may be considered as a collection of Dirac points. In the doped case, the Fermi surface has a torus shape and two independent processes of the momentum transfer contribute to the singular features of the polarizability even though we only have a single Fermi surface. In the static limit, there exist two independent singularities in the second derivative of the static polarizability. This results in the highly anisotropic Friedel oscillations which show the angle-dependent algebraic power law and the beat phenomena in the oscillatory electron density near a charged impurity. Furthermore, the dynamical polarizability has two singular lines along {\\hslash }ω =γ p and {\\hslash }ω =γ p{sin}η , where η is the angle between the external momentum {p} and the plane where the nodal ring lies. From the dynamical polarizability, we obtain the plasmon modes in the doped case, which show anisotropic dispersions and angle-dependent plasma frequencies. Qualitative differences between the low and high doping regimes are discussed in light of future experiments.
Friedel oscillation near a van Hove singularity in two-dimensional Dirac materials
NASA Astrophysics Data System (ADS)
Lu, Chi-Ken
2016-02-01
We consider Friedel oscillation in the two-dimensional Dirac materials when the Fermi level is near the van Hove singularity. Twisted graphene bilayer and the surface state of topological crystalline insulator are the representative materials which show low-energy saddle points that are feasible to probe by gating. We approximate the Fermi surface near saddle point with a hyperbola and calculate the static Lindhard response function. Employing a theorem of Lighthill, the induced charge density δ n due to an impurity is obtained and the algebraic decay of δ n is determined by the singularity of the static response function. Although a hyperbolic Fermi surface is rather different from a circular one, the static Lindhard response function in the present case shows a singularity similar with the response function associated with circular Fermi surface, which leads to the δ n\\propto {{R}-2} at large distance R. The dependences of charge density on the Fermi energy are different. Consequently, it is possible to observe in twisted graphene bilayer the evolution that δ n\\propto {{R}-3} near Dirac point changes to δ n\\propto {{R}-2} above the saddle point. Measurements using scanning tunnelling microscopy around the impurity sites could verify the prediction.
Friedel oscillation near a van Hove singularity in two-dimensional Dirac materials.
Lu, Chi-Ken
2016-02-17
We consider Friedel oscillation in the two-dimensional Dirac materials when the Fermi level is near the van Hove singularity. Twisted graphene bilayer and the surface state of topological crystalline insulator are the representative materials which show low-energy saddle points that are feasible to probe by gating. We approximate the Fermi surface near saddle point with a hyperbola and calculate the static Lindhard response function. Employing a theorem of Lighthill, the induced charge density [Formula: see text] due to an impurity is obtained and the algebraic decay of [Formula: see text] is determined by the singularity of the static response function. Although a hyperbolic Fermi surface is rather different from a circular one, the static Lindhard response function in the present case shows a singularity similar with the response function associated with circular Fermi surface, which leads to the [Formula: see text] at large distance R. The dependences of charge density on the Fermi energy are different. Consequently, it is possible to observe in twisted graphene bilayer the evolution that [Formula: see text] near Dirac point changes to [Formula: see text] above the saddle point. Measurements using scanning tunnelling microscopy around the impurity sites could verify the prediction.
Bao, Xiaoze; Wang, Baomin; Cui, Longchen; Zhu, Guodong; He, Yuli; Qu, Jingping; Song, Yuming
2015-11-06
A highly efficient and practical one-pot sequential process, consisting of an organocatalytic enantioselective Friedel-Crafts-type addition of 4-nonsubstituted pyrazolones to isatin-derived N-Boc ketimines and a subsequent diastereoselective fluorination of the pyrazolone moiety, is developed. This reaction sequence delivers novel oxindole-pyrazolone adducts featuring vicinal tetrasubstituted stereocenters with a 0.5 mol % catalyst loading in high yield with excellent enantio- and diastereocontrol. Notably, chloro, bromo, and thioether functionalities can be readily incorporated, rendering a broad diversity of the product.
Liu, Yongmei; Meng, Guangrong; Liu, Ruzhang; Szostak, Michal
2016-05-21
Highly chemoselective Friedel-Crafts acylation with twisted amides under mild conditions is reported for the first time. The reaction shows high functional group tolerance, obviating the need for preformed sensitive organometallic reagents and expensive transition metal catalysts. The high reactivity of amides is switched on by ground-state steric distortion to disrupt the amide bond nN→πCO* resonance as a critical design feature. Conceptually, this new acid-promoted mechanism of twisted amides provides direct access to bench-stable acylating reagents under mild, metal-free conditions.
Doan, Tan L H; Dao, Thong Q; Tran, Hai N; Tran, Phuong H; Le, Thach N
2016-05-04
A zirconium-based metal-organic framework, an effective heterogeneous catalyst, has been developed for the Friedel-Crafts benzoylation of aromatic compounds under microwave irradiation. Constructed by a Zr(iv) cluster and a linker 1,4-bis(2-[4-carboxyphenyl]ethynyl)benzene (H2CPEB), the MOF, possessing large pores and high chemical stability, was appropriate for the enhancement of Lewis acid activity under microwave irradiation. The reaction studies demonstrated that the material could give high yields for a few minutes and maintain its reactivity and structure over several cycles.
Gomes, Rafael F A; Coelho, Jaime A S; Frade, Raquel F M; Trindade, Alexandre F; Afonso, Carlos A M
2015-10-16
The first general protocol for the preparation of symmetric triarylmethanes bearing secondary anilines by ytterbium-catalyzed Friedel-Crafts reaction of hetero(aryl) aldehydes and secondary anilines is reported. Mechanistic studies indicated that the iminium ion intermediate is the electrophilic partner. The reaction is greatly accelerated by high pressure (9 kbar) and showed a broad substrate scope on the hetero(aryl) aldehyde. The new triarylmethanes exhibited activity against HT-29 cancer cell lines, with the best result scoring an IC50 of 1.74 μM.
Ranjbar, Sara; Riente, Paola; Rodríguez-Escrich, Carles; Yadav, Jagjit; Ramineni, Kishore; Pericàs, Miquel A
2016-04-01
Heterogenized versions of the second-generation MacMillan imidazolidin-4-one are described for the first time. This versatile organocatalyst has been supported on 1% DVB Merrifield resin and Fe3O4 magnetic nanoparticles through a copper-catalyzed alkyne-azide cycloaddition (CuAAC) reaction. The resulting catalytic materials have been successfully applied to the asymmetric Friedel-Crafts alkylation of indoles with α,β-unsaturated aldehydes. While both catalytic systems can be easily recovered and admit repeated recycling, the polystyrene-based catalyst shows higher stability and provides better stereoselectivities.
Ghosh, Arun K; Keyes, Chad; Veitschegger, Anne M
2014-07-23
Catalytic FeCl3 in the presence of 4Å molecular sieves has been shown to effect highly diastereoselective tandem Prins and Friedel-Crafts cyclization of substituted (E/Z)-6-phenylhex-3-en-1-ol and a variety of aldehydes to provide a range of polycyclic compounds in good to excellent yields. The reaction of an enantioenriched alcohol with an aldehyde provided the cyclization product without loss of optical activity. Furthermore, a Lewis acid catalyzed ring opening resulted in functionalized tetralin derivatives with multiple chiral centers.
Liu, Han; Xu, Jiaxi; Du, Da-Ming
2007-11-08
The first catalytic asymmetric Friedel-Crafts reaction of 2-methoxyfuran with nitroalkenes was developed under the catalysis of diphenylamine-tethered bis(oxazoline)-Zn(OTf)2 complexes. The reaction conditions and ligands were optimized, and the scope of the reaction was tested by varying the nitroalkenes. For most of aromatic and heteroaromatic nitroalkenes, good yields and high enantioselectivities (86-96% ee) were obtained. The methoxyfuran group in the product can be transformed to carboxylic acid via oxidative fragmentation with full retention of the configuration.
Wang, Wentao; Liu, Xiaohua; Cao, Weidi; Wang, Jun; Lin, Lili; Feng, Xiaoming
2010-02-01
A highly enantioselective Friedel-Crafts (F-C) alkylation of indoles and pyrrole with chalcone derivatives catalyzed by a chiral N,N'-dioxide-Sc(OTf)(3) complex has been developed that tolerates a wide range of substrates. The reaction proceeds in moderate to excellent yields and high enantioselectivities (85-92 % enantiomeric excess) using 2 mol % (for indole) or 0.5 mol % (for pyrrole) catalyst loading, which showed the potential value of the catalyst system. Meanwhile, a strong positive nonlinear effect was observed. On the basis of the experimental results and previous reports, a possible working model is proposed to explain the origin of the activation and asymmetric induction.
Xu, Chaoran; Zheng, Haifeng; Hu, Bowen; Liu, Xiaohua; Lin, Lili; Feng, Xiaoming
2017-08-29
An efficient atroposelective synthesis of axially chiral biaryldiols via asymmetric Friedel-Crafts aromatization between p-quinones and 2-naphthols was developed. A chiral cobalt(ii) complex of N,N'-dioxide enabled the process to generate axially chiral biaryldiols in up to 98% yield and 95% ee. A large range of substituents at different positions of p-quinones and 2-naphthols was tolerable. The configuration of the product and the chiral N,N'-dioxide-Co(ClO4)2 catalyst was identified by X-ray crystal diffraction analysis and a possible catalytic model was suggested.
Ricardo, Carolynne L; Mo, Xiaobin; McCubbin, J Adam; Hall, Dennis G
2015-03-09
The development of more general and efficient catalytic processes for Friedel-Crafts alkylations is an important objective of interest toward the production of pharmaceuticals and commodity chemicals. Herein, 2,3,4,5-tetrafluorophenylboronic acid was identified as a potent air- and moisture-tolerant metal-free catalyst that significantly improves the scope of direct Friedel-Crafts alkylations of a variety of slightly activated and neutral arenes, including polyarenes, with allylic and benzylic alcohols. This method also provides a simple alternative for the direct installation of prenyl units commonly found in naturally occurring arenes. Alkylations with benzylic alcohols occur under exceptionally mild conditions.
Sawama, Yoshinari; Asai, Shota; Kawajiri, Takahiro; Monguchi, Yasunari; Sajiki, Hironao
2015-01-26
Biaryl and heterobiaryl compounds are important frameworks across a range of fields including pharmaceutical and functional material chemistries. We have accomplished the efficient synthesis of various naphthalene-linked arenes and heteroarenes as biaryls and heterobiaryls by the FeCl3 -catalyzed Friedel-Crafts reactions accompanied by the ring-opening of the 1,4-epoxy moiety of 1,4-epoxy-1,4-dihydronaphthalenes. Especially, it is noteworthy that 1-silylated substrates were regioselectively transformed to the 3-aryl-1-silylnaphthalenes and the double Friedel-Crafts reactions using thiophene derivatives could directly produce the corresponding bis-naphthlated thiophene derivatives.
Tao, Yinsong; Wang, Baomin; Zhao, Jinfeng; Song, Yuming; Qu, Lihong; Qu, Jingping
2012-03-16
With the direct use of allylic alcohols as allylating agents, the Friedel-Crafts-type allylic alkylation of nitrogen-containing aromatic compounds catalyzed by a [Mo(3)S(4)Pd(η(3)-allyl)] cluster is achieved. With a 3 mol % catalyst loading in acetonitrile at reflux or 60 °C, a variety of N,N-dialkylanilines and indoles reacted smoothly with allylic alcohols to afford the Friedel-Crafts-type allylation products in good to excellent yields with high levels of regioselectivity.
A DFT study of the Al₂Cl₆-catalyzed Friedel-Crafts acylation of phenyl aromatic compounds.
Melissen, Sigismund T A G; Tognetti, Vincent; Dupas, Georges; Jouanneau, Julien; Lê, Guillaume; Joubert, Laurent
2013-11-01
The reaction pathways of several Friedel-Crafts acylations involving phenyl aromatic compounds were studied using density functional theory. The reactions were related to the Friedel-Crafts polycondensation of polyaryletherketones. In particular, the acylation of benzene with benzoyl chloride to form benzophenone and variations on this reaction were investigated. The acylation of benzene by one molecule of terephthaloyl chloride or isophthaloyl chloride as well as acylations at the m-, o-, and p-positions of diphenyl ether with one molecule of benzoyl chloride were studied. Adding an additional acyl chloride group to the electrophile appeared to have little influence on the reaction pathway, although the activation energy for the C-C bond-forming steps that occurred when isophthaloyl choride was used was different to the activation energy observed when terephthaloyl chloride was used. Upon changing the nucleophile to diphenyl ether, the reactivity changed according to the trend predicted on based on the o-, p-directing effects of the ether group. The deprotonation step that restored aromaticity varied widely according to the reaction. The rate-determining step in all of the studied reactions was the formation of the acylium ion, followed in importance by either the formation of the Wheland intermediate or the abstraction of hydrogen, depending on the reactivity of the nucleophile.
Zakharkin, L.I.; Anikina, E.V.
1987-08-20
In the Friedel-Crafts alkylation of benzene by normal 1-haloalkanes with three or more carbon atoms a mixture of phenylalkanes forms, due to isomerization of the alkyl chain and migration of a hydrogen atoms. Under analogous conditions the alkylation of benzene by omega-chloroalkanoic acids, Cl(CH/sub 2/)/sub n/COOH, and omega-bromoalkanonitriles proceeds with isomerization of the alkyl chain, but beginning only with 6-chlorohexanoic acid and 6-bromohexanonitrile. Such a difference in the behavior of these halogen derivatives has not received a convincing explanation, although the mechanism of Friedel-Crafts alkylation of benzene should be the same in the two cases. For a better understanding of this difference, this work presents a systematic study of benzene alkylation by 4-chlorobutyric, 5-chlorovaleric, 6-chlorohexanoic, and 7-chloroheptanoic acids and their methyl esters and nitriles, and by ..gamma..-butyro- and delta-valerolactones. The catalyst was crystalline AlCl/sub 3/ twice sublimed from Mg. For comparison, alkylation with the respective 1-chloroalkanes was carried out. In the alkylation of benzene by omega-chloroalkanoic acids Cl(CH/sub 2/)/sub n/COOH (where n = 3-6) and their methyl esters and nitriles, in the presence of AlCl/sub 3/, the degree of isomerization of the alkyl chain is less than with the corresponding 1-chloroalkanes, depending on the increase in electron acceptor activity in the sequence HOOC- > CH/sub 3/OCO- > CN-.
NASA Astrophysics Data System (ADS)
Ammar, Muhammad; Jiang, Sai; Ji, Shengfu
2016-01-01
A new strategy has been developed for the encapsulation of the phosphotungstic heteropoly acid (H3PW12O40 denoted as PTA) into zeolite imidazolate framework (ZIF-67) cage and the PTA@ZIF-67(ec) catalysts with different PTA content were prepared. The structure of the catalysts was characterized by XRD, BET, SEM, FT-IR, ICP-AES and TG. The catalytic activity and recovery properties of the catalysts for the Friedel-Crafts acylation of anisole with benzoyl chloride were evaluated. The results showed that 14.6-31.7 wt% PTA were encapsulated in the ZIF-67 cage. The PTA@ZIF-67(ec) catalysts had good catalytic activity for Friedel-Crafts acylation. The conversion of anisole can reach ~100% and the selectivity of the production can reach ~94% over 26.5 wt% PTA@ZIF-67(ec) catalyst under the reaction condition of 120 °C and 6 h. After reaction, the catalyst can be easily separated from the reaction mixture by the centrifugation. The recovered catalyst can be reused five times and the selectivity can be kept over 90%.
NASA Astrophysics Data System (ADS)
Wang, Tao; Tang, Fu Ming; Wu, Yi Fang
2011-09-01
Electron paramagnetic resonance and electron-nuclear double resonance methods were used to study the polycyclic aromatic radical cations produced in a Friedel-Crafts alkylating system, and the following radical cations were indentified: 3,6,11,14-tetramethyl dibenzo (a, c) triphylene and 2,6-dimethyl-9,10-di(p-methylbenzyl) anthracene radical cations. The results indicate that the observed electron paramagnetic resonance spectra are due to overcrowded polycyclic aromatic radical cations formed from the parent hydrocarbons. It is suggested that benzyl halides produced in the Friedel-Crafts alkylation reactions undergo Scholl condensation to give polycyclic aromatic hydrocarbons, which are converted into corresponding polycyclic aromatic radical cations in the presence of AlCl 3. We carried out the theoretical calculation of the isotropic 1H hyperfine coupling constants for studied both PAHs radical cations. The results indicate that the IEFPCM-DFT calculation at B3LYP level with 6-31++G(d,p), EPRII and EPRIII basis sets could well support the experimental hfcc assignment of the observed radicals. Optimized geometry indicates that the aromatic rings in both PAHs radical cations twisted significantly out of co-planarity.
ERIC Educational Resources Information Center
Dintzner, Matthew R.; Maresh, Justin J.; Kinzie, Charles R.; Arena, Anthony F.; Speltz, Thomas
2012-01-01
Students in the undergraduate organic laboratory synthesize tetrahydro-2-(4-nitrophenyl)-4-phenyl-2"H"-pyran via the Montmorillonite K10 clay-catalyzed reaction of p-nitrobenzaldehye with methanol, 3-buten-1-ol, and benzene. The synthesis comprises an environmentally friendly tandem Prins-Friedel-Crafts-type multicomponent reaction (MCR) and sets…
Sarvari, Mona Hosseini; Sharghi, Hashem
2004-10-01
Zinc oxide (ZnO) brings about a rapid Friedel-Crafts acylation of a range of activated and unactivated aromatic compounds such as anisole and chlorobenzene with acid chlorides in solvent-free conditions at room temperature. The ZnO powder can be reused up to three times after simple washing with dichloromethane. Copyright 2004 American Chemical Society
Nokami, Toshiki; Yamane, Yu; Oshitani, Shunsuke; Kobayashi, Jun-ka; Matsui, Shin-ichiro; Nishihara, Takashi; Uno, Hidemitsu; Hayase, Shuichi; Itoh, Toshiyuki
2015-06-19
Iron salt-catalyzed Friedel-Crafts alkylation of chiral α-aryl alcohols with a trimethylsilyl group was found to proceed with retention of the configuration of the hydroxyl group as a leaving group. The memory of chirality of this system stems from the β-silyl effect of the trimethylsilyl group on the carbocation intermediate.
Babu, K Naresh; Kinthada, Lakshmana K; Ghosh, Santanu; Bisai, Alakesh
2015-11-21
Simple and convenient Lewis acid-catalyzed Friedel-Crafts alkylations of 2-oxindoles as electron rich aromatics with 3-hydroxy-2-oxindoles as electron deficient partners have been developed. The reaction afforded a variety of dimeric 2-oxindoles with a C-3/C-5' linkage having an all-carbon quaternary center at the pseudobenzylic position in high yields.
Vila, Carlos; Quintero, Lucia; Blay, Gonzalo; Muñoz, M Carmen; Pedro, José R
2016-11-04
An efficient organocatalytic asymmetric synthesis of α-hydroxyketones has been developed. Quinine-derived thiourea catalyzed the enantioselective Friedel-Crafts alkylation of naphthols and activated phenols with aryl- and alkylglyoxal hydrates, providing the corresponding chiral α-hydroxyketones with high yields (up to 97%) and excellent enantioselectivities (up to 99% ee).
Zhou, Ding; Huang, Zheng; Yu, Xueting; Wang, Youxin; Li, Jian; Wang, Wei; Xie, Hexin
2015-11-20
A highly enantioselective aza-Friedel-Crafts (aza-F-C) reaction of cyclic trifluoromethyl ketimines and naphthols/phenols was developed with fluorenyl-substituted quinine-squaramide as the catalyst. This protocol enables direct access to biologically important chiral trifluoromethyl dihydroquinazolinones with up to 99% yields and up to 99% ee's.
Chen, Jian-Ping; Chen, Wen-Wen; Li, Yi; Xu, Ming-Hua
2015-03-21
A Lewis acid promoted highly diastereoselective asymmetric Friedel-Crafts alkylation of indoles with isatin-derived N-tert-butanesulfinyl ketimines is described. The reaction can be accomplished with ease in the presence of a catalytic amount of Bi(OTf)3, providing a series of 3-indolyl-3-aminooxindoles in excellent diastereoselectivities (up to 98% de) and yields (up to 99%).
de Graaff, C; Bensch, L; van Lint, Matthijs J; Ruijter, E; Orru, R V A
2015-10-28
The first o-iodoxybenzoic acid (IBX) mediated oxidation of unactivated amines to imines is described. A range of meso-pyrrolidines were shown to be suitable substrates. The chemical space was further explored with one-pot oxidative Ugi-type and aza-Friedel-Crafts reactions, which proved to be highly diastereoselective.
Zhu, Yu-Qin; Dong, Lin
2015-10-16
Ru(II)-catalyzed one-pot synthesis of polysubstituted spirofluorene-indenes via [3 + 2] annulation and then intramolecular Friedel-Crafts alkylation has been achieved. The simple method provides a broad scope of aryl ketones and internal alkynes, achieving PAHs skeletons in moderate to good yields.
NASA Astrophysics Data System (ADS)
Abed, Amel G.; Khalil, Salim M.
1999-04-01
MINDO-forces calculations have been performed on the uncatalysed and acid-catalysed Friedel-Crafts reaction between CH3F and CH4 . It has been found that the catalysed reaction is exothermic, spontaneous and has a smaller potential-energy barrier than the uncatalysed reaction. The mechanisms for uncatalysed and catalysed reactions are discussed.
Grach, Guillaume; Dinut, Aurelia; Marque, Sylvain; Marrot, Jérôme; Gil, Richard; Prim, Damien
2011-01-21
New Yb(OTf)(3)-pyridylalkylamine complexes have been employed as chiral Lewis acids in the enantioselective Friedel-Crafts alkylation of indole derivatives with trifluoropyruvates. The influence of the substituents as well as the configuration of the ligands have been studied and allowed us to reach enantiomeric excesses up to 83%.
ERIC Educational Resources Information Center
Dintzner, Matthew R.; Maresh, Justin J.; Kinzie, Charles R.; Arena, Anthony F.; Speltz, Thomas
2012-01-01
Students in the undergraduate organic laboratory synthesize tetrahydro-2-(4-nitrophenyl)-4-phenyl-2"H"-pyran via the Montmorillonite K10 clay-catalyzed reaction of p-nitrobenzaldehye with methanol, 3-buten-1-ol, and benzene. The synthesis comprises an environmentally friendly tandem Prins-Friedel-Crafts-type multicomponent reaction (MCR) and sets…
Ghosh, Santanu; Kinthada, Lakshmana K; Bhunia, Subhajit; Bisai, Alakesh
2012-10-18
A Lewis acid catalyzed Friedel-Crafts reaction of electron rich aromatics with 3-alkyl-3-hydroxy-2-oxindole (5) has been developed. The methodology provides a straightforward access to the core of azonazine (2) sharing an all-carbon quaternary stereocenter at the tetracyclic ring junction.
Removal of arsenic from water by Friedel's salt (FS: 3CaO·Al2O3·CaCl2·10H2O).
Zhang, Danni; Jia, Yongfeng; Ma, Jiayu; Li, Zhibao
2011-11-15
Low levels of arsenic can be effectively removed from water by adsorption onto various materials and searching for low-cost, high-efficiency new adsorbents has been a hot topic in recent years. In the present study, the performance of Friedel's salt (FS: 3CaO·Al(2)O(3)·CaCl(2)·10H(2)O), a layered double hydroxide (LDHs), as an adsorbent for arsenic removal from aqueous solution was investigated. Friedel's salt was synthesized at lower temperature (50°C) compared to traditional autoclave methods by reaction of calcium chloride with sodium aluminate. Kinetic study revealed that adsorption of arsenate by Friedel's salt was fast in the first 12h and equilibrium was achieved within 48 h. The adsorption kinetics are well described by second-order Lageren equation. The adsorption capacity of the synthesized sorbent for arsenate at pH 4 and 7 calculated from Langmuir adsorption isotherms was 11.85 and 7.80 mg/g, respectively. Phosphate and silicate markedly decreased the removal of arsenate, especially at higher pH, but sulfate was found to suppress arsenate adsorption at lower pH and the adverse effect was disappeared at pH ≥ 6. Common metal cations (Ca(2+), Mg(2+)) enhanced arsenate adsorption. The results suggest that Friedel's salt is a potential cost-effective adsorbent for arsenate removal in water treatment.
Zhang, Xiaoxiang; Teo, Wan Teng; Chan, Philip Wai Hong
2009-11-05
A method to prepare indenols efficiently by ytterbium(III) triflate catalyzed tandem Friedel-Crafts alkylation/hydroarylation of propargylic alcohols with phenols is described. The reaction was accomplished in moderate to excellent yields and regioselectivity under mild conditions and offers a straightforward and convenient one step synthetic route to bioactive indenols and its derivatives.
Alternating sums of reciprocal generalized Fibonacci numbers.
Kuhapatanakul, Kantaphon
2014-01-01
Recently Holliday and Komatsu extended the results of Ohtsuka and Nakamura on reciprocal sums of Fibonacci numbers to reciprocal sums of generalized Fibonacci numbers. The aim of this work is to give similar results for the alternating sums of reciprocals of the generalized Fibonacci numbers with indices in arithmetic progression. Finally we note our generalizations of some results of Holliday and Komatsu. Primary 11B37; secondary 11B39.
Fouvry, Étienne; Kowalski, Emmanuel; Michel, Philippe
2015-04-28
We give a general version of cancellation in exponential sums that arise as sums of products of trace functions satisfying a suitable independence condition related to the Goursat-Kolchin-Ribet criterion, in a form that is easily applicable in analytic number theory. © 2015 The Author(s) Published by the Royal Society. All rights reserved.
Fouvry, Étienne; Kowalski, Emmanuel; Michel, Philippe
2015-01-01
We give a general version of cancellation in exponential sums that arise as sums of products of trace functions satisfying a suitable independence condition related to the Goursat–Kolchin–Ribet criterion, in a form that is easily applicable in analytic number theory. PMID:25802414
Gauss Sum Factorization with Cold Atoms
Gilowski, M.; Wendrich, T.; Mueller, T.; Ertmer, W.; Rasel, E. M.; Jentsch, Ch.; Schleich, W. P.
2008-01-25
We report the first implementation of a Gauss sum factorization algorithm by an internal state Ramsey interferometer using cold atoms. A sequence of appropriately designed light pulses interacts with an ensemble of cold rubidium atoms. The final population in the involved atomic levels determines a Gauss sum. With this technique we factor the number N=263193.
NASA Astrophysics Data System (ADS)
Petrova, Galina P.; Ke, Zhuofeng; Park, Soyoung; Sugiyama, Hiroshi; Morokuma, Keiji
2014-04-01
The present theoretical investigation aims at understanding the origin of enantioselectivity of intramolecular Friedel-Crafts reaction, catalyzed by supramolecular Cu/DNA catalyst. 28 Conformations of the supramolecular L-Cu(II)-R/d(CAAAAATTTTTG)2 complex were thoroughly modeled to estimate their stability and structural features depending on the metal complex conformation and its intercalation position. The preferred formation of S-product can be rationalized by the higher binding energy of pro-S conformations to DNA. Pro-S conformations are structurally closer to the expected C3-C2‧ bond formation TS and usually not deeply buried into DNA, which would facilitate TS formation by decreasing the energy for conformational changes.
Yin, Qin; Klare, Hendrik F T; Oestreich, Martin
2017-03-20
In the electrophilic C-H borylation of electron-rich aromatic compounds with catecholborane, the catalytic generation of the boron electrophile is initiated by heterolysis of the B-H bond by various Lewis and Brønsted acids, with a boronium ion formed exclusively. After ligand dissociation, the corresponding borenium ion undergoes regioselective electrophilic aromatic substitution on aniline derivatives as well as nitrogen-containing heterocycles. The catalysis is optimized using B(C6 F5 )3 as the initiator and proceeds without the addition of an external base or dihydrogen acceptor. Temperatures above 80 °C are generally required to secure efficient turnover in these Friedel-Crafts-type reactions. Mechanistic experiments reveal that regeneration of the boronium/borenium ion with dihydrogen release is rate-determining. This finding finally led to the discovery that, with added alkenes, catalytic C-H borylations can, for the first time, be carried out at room temperature.
NASA Astrophysics Data System (ADS)
Chen, Yong; Qian, Jun; Teng, Xin; Zhang, Kan; Zhuang, Qixin; Han, Zhewen
2014-04-01
Etched multiwalled carbon nanotube (EMCNT) was prepared via an in situ reaction between Si and MCNT induced by the reaction between Na and I2. Subsequently, EMCNTs was subjected to a copolymerization reaction with 4,6-diaminoresorcinol salt (DAR·2HCl) and terephthalic acid (TA) in polyphosphoric acid (PPA) by Friedel-Crafts acylation reaction without any acid treatment or modification. The structure and morphology of the as-prepared poly(p-phenylene benzobisoxazole) (PBO)/EMCNT nanocomposites were characterized by x-ray diffraction (XRD), Raman spectra, and transmission electron microscopy (TEM). The scanning electronic microscope (SEM) images indicated that the EMCNTs can disperse in PBO matrix uniformly without agglomeration. And the electromagnetic properties of the obtained PBO/EMCNT nanocomposites characterized by vector network analyzer (VNA) showed that the introduced PBO/EMCNT composites exhibited a greater enhancement in dielectric loss and magnetic loss than PBO.
Zhao, Yun-Long; Lou, Qin-Xin; Wang, Long-Sheng; Hu, Wen-Hui; Zhao, Jun-Ling
2017-01-02
Naphthols and 3-trifluoroethylidene oxindoles were found to undergo an asymmetric Friedel-Crafts alkylation/lactonization reaction, catalyzed by only 2.5 mol % of a quinine-derived squaramide catalyst, to afford the corresponding α-aryl-β-trifluoromethyl dihydrocoumarin derivatives in high yields (up to 99 %) with excellent enantio- and diastereoselectivities (up to 98 % ee, >20:1 d.r.). Importantly, the lactonization proceeded by nucleophilic attack of the naphthol hydroxy group at the amide motif of the oxindoles under mild reaction conditions. This protocol represents a new strategy for the formation of dihydrocoumarins by an efficient intramolecular amide C-N bond-cleavage and esterification process.
Burke, Sarah J; Malachowski, William P; Mehta, Sharan K; Appenteng, Roselyn
2015-03-07
Due to the profound extent to which natural products inspire medicinal chemists in drug discovery, there is demand for innovative syntheses of these often complex materials. This article describes the synthesis of tricarbocyclic natural product architectures through an extension of the enantioselective Birch-Cope sequence with intramolecular Friedel-Crafts alkylation reactions. Additionally, palladium-catalyzed enol silane cycloalkenylation of the tricarbocyclic structures afforded the challenging bicyclo[3.2.1]octane C/D ring system found in the gibberellins and the ent-kauranes, two natural products with diverse medicinal value. In the case of the ent-kaurane derivative, an unprecedented alkene rearrangement converted four alkene isomers to one final product.
Entropy-Driven 1,2-Type Friedel-Crafts Reaction of Phenols with N-tert-Butoxycarbonyl Aldimines.
Kato, Masaru; Hirao, Shogo; Nakano, Katsuhiro; Sato, Makoto; Yamanaka, Masahiro; Sohtome, Yoshihiro; Nagasawa, Kazuo
2015-12-14
Differential activation entropy (ΔΔS(≠)) is revisited as an important parameter that governs catalytic stereodiscrimination processes by investigating temperature effects on the basis of the Eyring theory. However, correlating the ΔΔS(≠) effect and the molecular structure of the asymmetric catalyst is still an underdeveloped area. Efforts to identify factors (including catalyst structure, reactants, and reaction conditions) that contribute to the attainment of large ΔΔS(≠) values for enantioselective 1,2-type Friedel-Crafts reactions of phenols with N-tert-butoxycarbonyl aldimines catalyzed by conformationally flexible guanidine bisthioureas are described. First, we uncover an interesting property of the ΔΔS(≠)-driven stereodiscrimination process: maximum enantioselectivity is obtained at around room temperature. Second, a plausible transition-state model accounting for the characteristic ΔΔS(≠) effect and the structural dynamics of the conformationally flexible organocatalyst in the stereodiscrimination process is discussed.
Yin, Qin; Klare, Hendrik F T; Oestreich, Martin
2016-02-24
An electrophilic aromatic substitution (SE Ar) with a catalytically generated silicon electrophile is reported. Essentially any commercially available base-metal salt acts as an initiator/catalyst when activated with NaBAr(F)4. The thus-generated Lewis acid then promotes the SE Ar of electron-rich arenes with hydrosilanes but not halosilanes. This new C-H silylation was optimized for FeCl2/NaBAr(F)4, affording good yields at catalyst loadings as low as 0.5 mol %. The procedure is exceedingly straightforward and comes close to typical Friedel-Crafts methods, where no added base is needed to absorb the released protons.
Reddy, B V Subba; Venkateswarlu, A; Sridevi, B; Aldeyab, Salem S; Vinu, Ajayan
2015-09-01
Friedel-Crafts alkylation of electron-rich arenes with aldehydes has been achieved in the presence of an active and selective Amberlyst-15 catalyst at the reaction temperature of 60 degrees C in solvent-free conditions. The catalyst exhibits a very high activity and offers the corresponding triarylmethanes in excellent yields with a high selectivity. The use of highly reactive and selective Amberlyist-15 makes this procedure simple, convenient, cost-effective, practical and environmentally friendly. This method provides an easy access to triarylmethanes in a single step using a readily available acidic ionic resin, which is a stable and easy to separate from the reaction mixture by a simple filtration technique.
Burke, Sarah J.; Mehta, Sharan K.; Appenteng, Roselyn
2015-01-01
Due to the profound extent to which natural products inspire medicinal chemists in drug discovery, there is demand for innovative syntheses of these often complex materials. This article describes the synthesis of tricarbocyclic natural product architectures through an extension of the enantioselective Birch-Cope sequence with intramolecular Friedel-Crafts alkylation reactions. Additionally, palladium-catalyzed enol silane cycloalkenylation of the tricarbocyclic structures afforded the challenging bicyclo[3.2.1]octane C/D ring system found in the gibberellins and the ent-kauranes, two natural products with diverse medicinal value. In the case of the ent-kaurane derivative, an unprecedented alkene rearrangement converted four alkene isomers to one final product. PMID:25598198
A new sum analogous to Gauss sums and its fourth power mean.
Ru, Shaofeng; Zhang, Wenpeng
2014-01-01
The main purpose of this paper is to use the analytic methods and the properties of Gauss sums to study the computational problem of one kind of new sum analogous to Gauss sums and give an interesting fourth power mean and a sharp upper bound estimate for it.
Fenster, Erik; Fehl, Charlie; Aubé, Jeffrey
2011-01-01
A tandem Prins/Friedel-Crafts reaction useful for the construction of the indeno-tetrahydropyridine core of the haouamine alkaloids and a formal synthesis of (−)-haouamine A are described. PMID:21517105
NASA Astrophysics Data System (ADS)
Schuetz, W.; Heuler, P.
1994-03-01
In the first sections, the requirements to be met by hypotheses for fatigue life prediction (including those for the crack initiation and crack propagation phases) are discussed in detail. These requirements are shown to be different for 'scientific' and for 'industrial' fatigue life prediction. Aspects with regard to an assessment of fatigue life prediction hypotheses are discussed. The last section presents the results of a large cooperative program between IABG and several automobile manufacturers, in which Miner's Rule in several versions was assessed against spectrum tests with five different actual automobile components: forged steel stub axle; forged steel stub axle, induction hardened; sheet steel welded rear axle (front wheel drive car); cast aluminum wheel; and welded sheet steel wheel. Since up to 80 components each were available, and two different, but typical, automotive stress-time histories were employed, the assessment was very thorough, avoiding many of the drawbacks of previous assessments. It is shown that damage sums to failure were usually far below 1.0; they also depended on the component in question, the aluminum wheel resulting in the lowest damage sums to failure; the damage sums to failure where always lower for a mild spectrum than for a severe one; and the influence of spectrum variation was predicted best - among the hypotheses tested - by use of a recent proposal of Zenner and Liu.
Robey, Robert
2015-10-06
This code is a set of global sums to support the paper "Computational Reproducibility for Production Physics Applications" submitted to the Numerical Reproducibility at Exascale (NRE 2015) workshop at the 2015 Supercomputing conference, Nov. 20, 2015
NMR Experiment Factors Numbers with Gauss Sums
NASA Astrophysics Data System (ADS)
Mehring, Michael; Müller, Klaus; Averbukh, Ilya Sh.; Merkel, Wolfgang; Schleich, Wolfgang P.
2007-03-01
We factor the number 157573 using an NMR implementation of Gauss sums. Although the current implementation is classical and scales exponentially, we believe that an extension to the quantum regime using entangled states is possible.
NASA Astrophysics Data System (ADS)
Höppner, Frank
Association rules are rules of the kind "70% of the customers who buy vine and cheese also buy grapes". While the traditional field of application is market basket analysis, association rule mining has been applied to various fields since then, which has led to a number of important modifications and extensions. We discuss the most frequently applied approach that is central to many extensions, the Apriori algorithm, and briefly review some applications to other data types, well-known problems of rule evaluation via support and confidence, and extensions of or alternatives to the standard framework.
Support activities to maintain SUMS flight readiness
NASA Technical Reports Server (NTRS)
Wright, Willie
1992-01-01
The Shuttle Upper Atmosphere Mass Spectrometer (SUMS), a component experiment of the NASA Orbital Experiments Program (OEX), was flown aboard the shuttle Columbia (OV102) mounted at the forward end of the nose landing gear well with an atmospheric gas inlet system fitted to the lower fuselage (chin panel) surface. The SUMS was designed to provide atmospheric data in flow regimes inaccessible prior to the development of the Space Transportation System (STS). The experiment mission operation began about one hour prior to shuttle de-orbit entry maneuver and continued until reaching 1.6 torr (about 86 km altitude). The SUMS mass spectrometer consists of the spare unit from the Viking mission to Mars. Bendix Aerospace under contract to NASA LaRC incorporated the Viking mass spectrometer, a microprocessor based logic card, a pressurized instrument case, and the University of Texas at Dallas provided a gas inlet system into a configuration suited to interface with the shuttle Columbia. The SUMS experiment underwent static and dynamic calibration as well as vacuum maintenance before and after STS 40 shuttle flight. The SUMS flew a total of 3 times on the space shuttle Columbia. Between flights the SUMS was maintained in flight ready status. The flight data has been analyzed by the NASA LaRC Aerothermodynamics Branch. Flight data spectrum plots and reports are presented in the Appendices to the Final Technical Report for NAS1-17399.
Support activities to maintain SUMS flight readiness
NASA Astrophysics Data System (ADS)
Wright, Willie
1992-05-01
The Shuttle Upper Atmosphere Mass Spectrometer (SUMS), a component experiment of the NASA Orbital Experiments Program (OEX), was flown aboard the shuttle Columbia (OV102) mounted at the forward end of the nose landing gear well with an atmospheric gas inlet system fitted to the lower fuselage (chin panel) surface. The SUMS was designed to provide atmospheric data in flow regimes inaccessible prior to the development of the Space Transportation System (STS). The experiment mission operation began about one hour prior to shuttle de-orbit entry maneuver and continued until reaching 1.6 torr (about 86 km altitude). The SUMS mass spectrometer consists of the spare unit from the Viking mission to Mars. Bendix Aerospace under contract to NASA LaRC incorporated the Viking mass spectrometer, a microprocessor based logic card, a pressurized instrument case, and the University of Texas at Dallas provided a gas inlet system into a configuration suited to interface with the shuttle Columbia. The SUMS experiment underwent static and dynamic calibration as well as vacuum maintenance before and after STS 40 shuttle flight. The SUMS flew a total of 3 times on the space shuttle Columbia. Between flights the SUMS was maintained in flight ready status. The flight data has been analyzed by the NASA LaRC Aerothermodynamics Branch. Flight data spectrum plots and reports are presented in the Appendices to the Final Technical Report for NAS1-17399.
Sohtome, Yoshihiro; Shin, Bongki; Horitsugi, Natsuko; Noguchi, Keiichi; Nagasawa, Kazuo
2011-09-05
Herein, we present details of our conformationally flexible, 1,3-diamine-tethered guanidine/bisthiourea organocatalysts for chemo-, regio-, and enantioselective 1,4-type Friedel-Crafts reactions of phenols. These organocatalysts show a unique stereo-discrimination governed by the differential activation entropy (ΔΔS(≠)), rather than by the differential activation enthalpy (ΔΔH(≠)). Extensive kinetic analyses using Eyring plots for a series of guanidine/bisthiourea organocatalysts revealed the key structural motif in the catalysts associated with a large magnitude of differential activation entropy (ΔΔS(≠)). A plausible guanidine-thiourea cooperative mechanism for the enantioselective Friedel-Crafts reaction is proposed.
Akagawa, Kengo; Umezawa, Ryota; Kudo, Kazuaki
2012-01-01
In the presence of a peptide catalyst and the oxidative enzyme laccase, a one-pot sequential reaction including a Friedel-Crafts-type alkylation of α,β-unsaturated aldehydes followed by an α-oxyamination was realized. The reaction in aqueous solvent to promote the enzymatic oxidation, and the use of a peptide catalyst compatible with such conditions, were essential. The present sequential reaction afforded oxygen-functionalized indole or pyrrole derivatives in a highly enantioselective manner.
Sun, Yongqing; Qiao, Yu; Zhao, Haiying; Li, Baoguo; Chen, Shufeng
2016-12-02
An efficient and concise Cu(OTf)2-catalyzed Friedel-Crafts alkylation/annulation cascade reaction of substituted indoles with 1,2-dicarbonyl-3-enes has been established. This reaction uses readily available starting materials and is operationally simple, thus representing a practical method for the construction of diverse 9H-pyrrolo[1,2-a]indoles bearing a carbonyl group.
Kumar, Anand; Thadkapally, Srinivas; Menon, Rajeev S
2015-11-06
Cesium carbonate-mediated reaction of 2-hydroxybenzaldehydes and 2-bromoallyl sulfones afforded 2H- and 4H-chromenol derivatives endowed with a 3-arylsulfonyl group. 2-Bromoallyl sulfones functioned as synthetic equivalents of allenyl sulfones under these conditions. The 2H- and 4H-chromenol derivatives underwent regioselective Friedel-Crafts reactions with heteroarenes in the presence of p-toluenesulfonic acid to afford 4-heteroaryl-4H-chromene derivatives in excellent yields.
Zhang, Yulong; Yang, Na; Liu, Xiaohua; Guo, Jing; Zhang, Xiying; Lin, Lili; Hu, Changwei; Feng, Xiaoming
2015-05-18
Chiral Ni(ii)-complexes of N,N'-dioxides show high catalytic activity and enantioselectivity in catalysing the asymmetric Friedel-Crafts C3-alkylation of 2,5-dimethyl pyrrole to β,γ-unsaturated α-ketoesters. A dramatic reversal of enantioselectivity is realized with ligands derived from the same type of chiral source of l-ramipril, by slightly tuning the amide units.
Bi, Bo; Lou, Qin-Xin; Ding, Yu-Yang; Chen, Sheng-Wei; Zhang, Sha-Sha; Hu, Wen-Hui; Zhao, Jun-Ling
2015-02-06
A highly enantioselective C2 Friedel-Crafts alkylation reaction of 3-substituted indoles to β,γ-unsaturated α-ketimino esters has been developed. This reaction was efficiently catalyzed by a chiral phosphoric acid catalyst. The corresponding C2-substituted indole derivatives, bearing an α-ketimino ester motif, were obtained in moderate to high yields (up to 93%) and with high enantioselectivities (up to >99% ee).
He, Yuwei; Lin, Maohui; Li, Zhongmin; Liang, Xinting; Li, Guilong; Antilla, Jon C
2011-09-02
The direct asymmetric intramolecular aza-Friedel-Crafts reaction of N-aminoethylpyrroles with aldehydes catalyzed by a chiral phosphoric acid represents the first efficient method for the preparation of medicinally interesting chiral 1,2,3,4-tetrahydropyrrolo[1,2-a]pyrazines with high yields and high enantioselectivities. This strategy has been shown to be quite general toward various aldehydes and pyrrole derivatives.
Liu, Yanling; Shang, Deju; Zhou, Xin; Liu, Xiaohua; Feng, Xiaoming
2009-01-01
An efficient catalytic asymmetric Friedel-Crafts alkylation of indoles with alkylidene malonates has been developed by using a chiral N,N'-dioxide-Sc(OTf)(3) complex as the catalyst (see scheme). Some optically active intermediates containing the indole skeleton have been synthesized, such as indolepropionic acid, tryptamines, and beta-carbolines. The coordination between the scandium atom and the chiral N,N'-dioxide compound has been revealed by X-ray structure analysis.
Enders, Dieter; Wang, Chuan; Mukanova, Meruyert; Greb, Andreas
2010-04-14
A new organocatalytic quadruple domino Friedel-Crafts-type/Michael/Michael/aldol condensation reaction has been developed. In this one-pot multi-component process acrolein, various indoles and nitroalkenes are used as starting materials. The diphenylprolinol TMS-ether catalysis provides a straightforward and efficient entry to 3-(cyclohexenylmethyl)-indoles bearing three stereogenic centers in moderate to excellent yields (23-82%) and excellent stereoselectivities (dr = 91 : 9 to >95 : 5, ee = 94 to >99%).
Jadhav, Arvind H; Chinnappan, Amutha; Hiremath, Vishwanath; Seo, Jeong Gil
2015-10-01
Aluminum trichloride (AlCl3) impregnated molybdenum oxide heterogeneous nano-catalyst was prepared by using simple impregnation method. The prepared heterogeneous catalyst was characterized by powder X-ray diffraction, FT-IR spectroscopy, solid-state NMR spectroscopy, SEM imaging, and EDX mapping. The catalytic activity of this protocol was evaluated as heterogeneous catalyst for the Friedel-Crafts acylation reaction at room temperature. The impregnated MoO4(AlCl2)2 catalyst showed tremendous catalytic activity in Friedel-Crafts acylation reaction under solvent-free and mild reaction condition. As a result, 84.0% yield of acyl product with 100% consumption of reactants in 18 h reaction time at room temperature was achieved. The effects of different solvents system with MoO4(AlCl2)2 catalyst in acylation reaction was also investigated. By using optimized reaction condition various acylated derivatives were prepared. In addition, the catalyst was separated by simple filtration process after the reaction and reused several times. Therefore, heterogeneous MoO4(AlCl2)2 catalyst was found environmentally benign catalyst, very convenient, high yielding, and clean method for the Friedel-Crafts acylation reaction under solvent-free and ambient reaction condition.
Randomly stopped sums: models and psychological applications
Smithson, Michael; Shou, Yiyun
2014-01-01
This paper describes an approach to modeling the sums of a continuous random variable over a number of measurement occasions when the number of occasions also is a random variable. A typical example is summing the amounts of time spent attending to pieces of information in an information search task leading to a decision to obtain the total time taken to decide. Although there is a large literature on randomly stopped sums in financial statistics, it is largely absent from psychology. The paper begins with the standard modeling approaches used in financial statistics, and then extends them in two ways. First, the randomly stopped sums are modeled as “life distributions” such as the gamma or log-normal distribution. A simulation study investigates Type I error rate accuracy and power for gamma and log-normal versions of this model. Second, a Bayesian hierarchical approach is used for constructing an appropriate general linear model of the sums. Model diagnostics are discussed, and three illustrations are presented from real datasets. PMID:25426090
Merle, Géraldine; Ioana, Filipoi Carmen; Demco, Dan Eugen; Saakes, Michel; Hosseiny, Seyed Schwan
2013-12-30
Highly conductive and low vanadium permeable crosslinked sulfonated poly(ether ether ketone) (cSPEEK) membranes were prepared by electrophilic aromatic substitution for a Vanadium/Air Redox Flow Battery (Vanadium/Air-RFB) application. Membranes were synthesized from ethanol solution and crosslinked under different temperatures with 1,4-benzenedimethanol and ZnCl2 via the Friedel-Crafts crosslinking route. The crosslinking mechanism under different temperatures indicated two crosslinking pathways: (a) crosslinking on the sulfonic acid groups; and (b) crosslinking on the backbone. It was observed that membranes crosslinked at a temperature of 150 °C lead to low proton conductive membranes, whereas an increase in crosslinking temperature and time would lead to high proton conductive membranes. High temperature crosslinking also resulted in an increase in anisotropy and water diffusion. Furthermore, the membranes were investigated for a Vanadium/Air Redox Flow Battery application. Membranes crosslinked at 200 °C for 30 min with a molar ratio between 2:1 (mol repeat unit:mol benzenedimethanol) showed a proton conductivity of 27.9 mS/cm and a 100 times lower VO2+ crossover compared to Nafion.
García-Fernández, Almudena; Megens, Rik P; Villarino, Lara; Roelfes, Gerard
2016-12-21
DNA-induced rate acceleration has been identified as one of the key elements for the success of the DNA-based catalysis concept. Here we report on a novel DNA-based catalytic Friedel-Crafts conjugate addition/enantioselective protonation reaction in water, which represents the first example of a reaction that critically depends on the >700- to 990-fold rate acceleration caused by the presence of a DNA scaffold. The DNA-induced rate acceleration observed is the highest reported due to the environment presented by a biomolecular scaffold for any hybrid catalyst, to date. Based on a combination of kinetics and binding studies, it is proposed that the rate acceleration is in part due to the DNA acting as a pseudophase, analogous to micelles, in which all reaction components are concentrated, resulting in a high effective molarity. The involvement of additional second coordination sphere interactions is suggested by the enantioselectivity of the product. The results presented here show convincingly that the DNA-based catalysis concept, thanks to the DNA-accelerating effect, can be an effective approach to achieving a chemically challenging reaction in water.
Fan, Aili; Xie, Xiulan; Li, Shu-Ming
2015-07-21
Tryptophan prenyltransferases FgaPT2, 5-DMATS, 6-DMATSSv and 7-DMATS catalyse regiospecific C-prenylations on the indole ring, while tyrosine prenyltransferases SirD and TyrPT catalyse the O-prenylation of the phenolic hydroxyl group. In this study, we report the Friedel-Crafts alkylation of L-o-tyrosine by these enzymes. Surprisingly, no conversion was detected with SirD and three tryptophan prenyltransferases showed significantly higher activity than another tyrosine prenyltransferase TyrPT. C5-prenylated L-o-tyrosine was identified as a unique product of these enzymes. Using L-m-tyrosine as the prenylation substrate, product formation was only observed with the tryptophan prenyltransferases FgaPT2 and 7-DMATS. C4- and C6-prenylated derivatives were identified in the reaction mixture of FgaPT2. These results provided additional evidence for the similarities and differences between these two subgroups within the DMATS superfamily in their catalytic behaviours.
NASA Astrophysics Data System (ADS)
Akhrem, Irena S.; Orlinkov, Alexander V.; Vol'pin, Mark E.
1996-10-01
The results of studies on direct functionalisation of activated alkanes and cycloalkanes under the action of 'classical' Friedel-Crafts complexes (viz. equimolar complexes of acyl halides with aluminium halides) and related systems containing smaller or somewhat larger amounts of aluminium halide are surveyed. The studies carried out during the last decade on functionalisation of saturated hydrocarbons devoid of tertiary carbon atoms, by aprotic organic superacids RCOX . 2AlCl3 are summarised. Reactions of alkanes with acylium cations in superacidic media are considered. The published data on the structure of complexes RCOX . AlCl3 and RCOX . 2AlCl3 and on the nature of the active complexes in the reactions of arenes with acylium cations and with complexes RCOX . AlCl3 in both acidic and organic media as well as in the reactions of alkanes with acylium salts in protic superacids and with superacidic complexes RCOX . 2AlCl3 in aprotic solvents are analysed. The prospects for the synthesis of organic compounds from alkanes and cycloalkanes under the action of complexes of acyl halides with aluminium halides are outlined. The bibliography includes 128 references.
Nagaraj, Anbu; Amarajothi, Dhakshinamoorthy
2017-05-15
In the present work, Friedel-Crafts alkylation reaction of indole with β-nitrostyrene is examined using a readily available copper based metal-organic frameworks (MOFs) namely, Cu3(BTC)2 (BTC: 1,3,5-benzenetricarboxylic acid) as solid catalyst under mild reaction conditions. Among the various catalysts screened for this reaction, Cu3(BTC)2 exhibits higher activity under the optimized reaction conditions. Besides the absence of leaching of active sites, it is also observed that the catalyst can be reused for four cycles with a minimal decrease in its activity. Cu3(BTC)2 is used as a catalyst to synthesise a series of heterocyclic compounds with different indole and β-nitrostyrene derivatives in moderate to high yields. The present catalytic system shows comparable activity against to recent reports but the advantage of Cu3(BTC)2 is that it does not require any post-functionalization and above all it can be readily synthesised, thus contributing to the synthesis of heterocyclic compounds with high biological interest.
Selvin, Rosilda; Roselin, L Selva; Khayyat, Suzan A; Umar, Ahmad
2013-06-01
P-Methyacetophenone, the acylated product of toluene finds a wide range of applications in the flavors and fragrance industry. It is typically produced on an industrial scale by Friedel-Crafts acylation of toluene with acetic anhydride using homogeneous, corrosive and polluting acid catalysts such as aluminium chloride. The pollution problems related to this process such as the disposal of catalyst and treatment of acidic effluent needs to be replaced by a green process. The current work reports on the activity of hierarchical zeolite Beta in the liquid phase acylation of toluene with acetic anhydride. The liquid phase reactions were carried out in the temperature range of 60-140 degrees C in an autoclave. The effect of various reaction parameters such as time-on-stream (TOS), mole ratio of reactants, catalyst loading, and reaction temperature on the rates of reaction has been investigated. Under the optimum reaction conditions the performance of hierarchical zeolite Beta was compared with nanocrystalline zeolite Beta. It was found that hierarchical zeolite Beta catalyst exhibit higher activity, which is due to the hierarchical porosity and to the nano size of the Beta zeolite catalyst particles allows faster diffusion of the products out of the catalyst.
Rosana, Michael R; Hunt, Jacob; Ferrari, Anthony; Southworth, Taylor A; Tao, Yuchuan; Stiegman, Albert E; Dudley, Gregory B
2014-08-15
Thermally promoted Friedel-Crafts benzylation of arene solvents has been examined under both conventional convective heating with an oil bath and heating using microwave (MW) energy. Bulk solution temperatures-as measured by internal and external temperature probes and as defined by solvent reflux-were comparable in both sets of experiments. MW-specific rate enhancements were documented under certain conditions and not others. The observed rate enhancements at a given temperature are proposed to arise from selective MW heating of polar solutes, perturbing thermal equilibrium between the solute and bulk solution. Central to MW-specific thermal phenomena is the difference between heat and temperature. Temperature is a measure of the ensemble average kinetic molecular energy of all solution components, but temperature does not provide information about solute-specific energy differences that may arise as a consequence of selective MW heating. Enhanced chemical reactivity of the MW-absorbing solute can be described as a MW-specific "extra-temperature thermal effect", because the measurable solution temperature only captures a portion of the solute kinetic molecular energy. Experimental factors that favor MW-specific rate enhancements are discussed with an eye toward future development of MW-actuated organic reactions, in which the observed thermal reactivity exceeds what is predicted from temperature-based Arrhenius calculations.
Méndez, Isabel; Rodríguez, Ricardo; Polo, Víctor; Passarelli, Vincenzo; Lahoz, Fernando J; García-Orduña, Pilar; Carmona, Daniel
2016-07-25
By changing the temperature from 283 to 233 K, the S (99 % ee) or R (96 % ee) enantiomer of the Friedel-Crafts (FC) adduct of the reaction between N-methyl-2-methylindole and trans-β-nitrostyrene can be obtained by using (SRh ,RC )-[(η(5) -C5 Me5 )Rh{(R)-Prophos}(H2 O)][SbF6 ]2 as the catalyst precursor. This catalytic system presents two other uncommon features: 1) The ee changes with reaction time showing trends that depend on the reaction temperature and 2) an increase in the catalyst loading results in a decrease in the ee of the S enantiomer. Detection and characterization of the intermediate metal-nitroalkene and metal-aci-nitro complexes, the free aci-nitro compound, and the FC adduct-complex, together with solution NMR measurements, theoretical calculations, and kinetic studies have allowed us to propose two plausible alternative catalytic cycles. On the basis of these cycles, all the above-mentioned observations can be rationalized. In particular, the reversibility of one of the cycles together with the kinetic resolution of the intermediate aci-nitro complexes account for the high ee values achieved in both antipodes. On the other hand, the results of kinetic measurements explain the unusual effect of the increment in catalyst loading.
Kobayashi, Amane; Sekiguchi, Yuki; Takayama, Yuki; Oroguchi, Tomotaka; Nakasako, Masayoshi
2014-11-17
Coherent X-ray diffraction imaging (CXDI) is a lensless imaging technique that is suitable for visualizing the structures of non-crystalline particles with micrometer to sub-micrometer dimensions from material science and biology. One of the difficulties inherent to CXDI structural analyses is the reconstruction of electron density maps of specimen particles from diffraction patterns because saturated detector pixels and a beam stopper result in missing data in small-angle regions. To overcome this difficulty, the dark-field phase-retrieval (DFPR) method has been proposed. The DFPR method reconstructs electron density maps from diffraction data, which are modified by multiplying Gaussian masks with an observed diffraction pattern in the high-angle regions. In this paper, we incorporated Friedel centrosymmetry for diffraction patterns into the DFPR method to provide a constraint for the phase-retrieval calculation. A set of model simulations demonstrated that this constraint dramatically improved the probability of reconstructing correct electron density maps from diffraction patterns that were missing data in the small-angle region. In addition, the DFPR method with the constraint was applied successfully to experimentally obtained diffraction patterns with significant quantities of missing data. We also discuss this method's limitations with respect to the level of Poisson noise in X-ray detection.
On the sum of generalized Fibonacci sequence
NASA Astrophysics Data System (ADS)
Chong, Chin-Yoon; Ho, C. K.
2014-06-01
We consider the generalized Fibonacci sequence {Un defined by U0 = 0, U1 = 1, and Un+2 = pUn+1+qUn for all n∈Z0+ and p, q∈Z+. In this paper, we derived various sums of the generalized Fibonacci sequence from their recursive relations.
Fibonacci Identities via the Determinant Sum Property
ERIC Educational Resources Information Center
Spivey, Michael
2006-01-01
We use the sum property for determinants of matrices to give a three-stage proof of an identity involving Fibonacci numbers. Cassini's and d'Ocagne's Fibonacci identities are obtained at the ends of stages one and two, respectively. Catalan's Fibonacci identity is also a special case.
Fibonacci Identities via the Determinant Sum Property
ERIC Educational Resources Information Center
Spivey, Michael
2006-01-01
We use the sum property for determinants of matrices to give a three-stage proof of an identity involving Fibonacci numbers. Cassini's and d'Ocagne's Fibonacci identities are obtained at the ends of stages one and two, respectively. Catalan's Fibonacci identity is also a special case.
A Strategy for Replacing Sum Scoring
ERIC Educational Resources Information Center
Ramsay, James O.; Wiberg, Marie
2017-01-01
This article promotes the use of modern test theory in testing situations where sum scores for binary responses are now used. It directly compares the efficiencies and biases of classical and modern test analyses and finds an improvement in the root mean squared error of ability estimates of about 5% for two designed multiple-choice tests and…
Karatsuba's method for estimating Kloosterman sums
NASA Astrophysics Data System (ADS)
Korolev, M. A.
2016-08-01
Using Karatsuba's method, we obtain estimates for Kloosterman sums modulo a prime, in which the number of terms is less than an arbitrarily small fixed power of the modulus. These bounds refine similar results obtained earlier by Bourgain and Garaev. Bibliography: 16 titles.
Summing threshold logs in a parton shower
NASA Astrophysics Data System (ADS)
Nagy, Zoltán; Soper, Davison E.
2016-10-01
When parton distributions are falling steeply as the momentum fractions of the partons increases, there are effects that occur at each order in α s that combine to affect hard scattering cross sections and need to be summed. We show how to accomplish this in a leading approximation in the context of a parton shower Monte Carlo event generator.
van Veelen, Matthijs; Allen, Benjamin; Hoffman, Moshe; Simon, Burton; Veller, Carl
2017-02-07
This paper reviews and addresses a variety of issues relating to inclusive fitness. The main question is: are there limits to the generality of inclusive fitness, and if so, what are the perimeters of the domain within which inclusive fitness works? This question is addressed using two well-known tools from evolutionary theory: the replicator dynamics, and adaptive dynamics. Both are combined with population structure. How generally Hamilton's rule applies depends on how costs and benefits are defined. We therefore consider costs and benefits following from Karlin and Matessi's (1983) "counterfactual method", and costs and benefits as defined by the "regression method" (Gardner et al., 2011). With the latter definition of costs and benefits, Hamilton's rule always indicates the direction of selection correctly, and with the former it does not. How these two definitions can meaningfully be interpreted is also discussed. We also consider cases where the qualitative claim that relatedness fosters cooperation holds, even if Hamilton's rule as a quantitative prediction does not. We furthermore find out what the relation is between Hamilton's rule and Fisher's Fundamental Theorem of Natural Selection. We also consider cancellation effects - which is the most important deepening of our understanding of when altruism is selected for. Finally we also explore the remarkable (im)possibilities for empirical testing with either definition of costs and benefits in Hamilton's rule.
Separating OR, SUM, and XOR Circuits.
Find, Magnus; Göös, Mika; Järvisalo, Matti; Kaski, Petteri; Koivisto, Mikko; Korhonen, Janne H
2016-08-01
Given a boolean n × n matrix A we consider arithmetic circuits for computing the transformation x ↦ Ax over different semirings. Namely, we study three circuit models: monotone OR-circuits, monotone SUM-circuits (addition of non-negative integers), and non-monotone XOR-circuits (addition modulo 2). Our focus is on separating OR-circuits from the two other models in terms of circuit complexity: We show how to obtain matrices that admit OR-circuits of size O(n), but require SUM-circuits of size Ω(n(3/2)/log(2)n).We consider the task of rewriting a given OR-circuit as a XOR-circuit and prove that any subquadratic-time algorithm for this task violates the strong exponential time hypothesis.
Second harmonic generation and sum frequency generation
Pellin, M.J.; Biwer, B.M.; Schauer, M.W.; Frye, J.M.; Gruen, D.M.
1990-01-01
Second harmonic generation and sum frequency generation are increasingly being used as in situ surface probes. These techniques are coherent and inherently surface sensitive by the nature of the mediums response to intense laser light. Here we will review these two techniques using aqueous corrosion as an example problem. Aqueous corrosion of technologically important materials such as Fe, Ni and Cr proceeds from a reduced metal surface with layer by layer growth of oxide films mitigated by compositional changes in the chemical makeup of the growing film. Passivation of the metal surface is achieved after growth of only a few tens of atomic layers of metal oxide. Surface Second Harmonic Generation and a related nonlinear laser technique, Sum Frequency Generation have demonstrated an ability to probe the surface composition of growing films even in the presence of aqueous solutions. 96 refs., 4 figs.
Strong sum distance in fuzzy graphs.
Tom, Mini; Sunitha, Muraleedharan Shetty
2015-01-01
In this paper the idea of strong sum distance which is a metric, in a fuzzy graph is introduced. Based on this metric the concepts of eccentricity, radius, diameter, center and self centered fuzzy graphs are studied. Some properties of eccentric nodes, peripheral nodes and central nodes are obtained. A characterisation of self centered complete fuzzy graph is obtained and conditions under which a fuzzy cycle is self centered are established. We have proved that based on this metric, an eccentric node of a fuzzy tree G is a fuzzy end node of G and a node is an eccentric node of a fuzzy tree if and only if it is a peripheral node of G and the center of a fuzzy tree consists of either one or two neighboring nodes. The concepts of boundary nodes and interior nodes in a fuzzy graph based on strong sum distance are introduced. Some properties of boundary nodes, interior nodes and complete nodes are studied.
A 2-categorical state sum model
Baratin, Aristide; Freidel, Laurent
2015-01-15
It has long been argued that higher categories provide the proper algebraic structure underlying state sum invariants of 4-manifolds. This idea has been refined recently, by proposing to use 2-groups and their representations as specific examples of 2-categories. The challenge has been to make these proposals fully explicit. Here, we give a concrete realization of this program. Building upon our earlier work with Baez and Wise on the representation theory of 2-groups, we construct a four-dimensional state sum model based on a categorified version of the Euclidean group. We define and explicitly compute the simplex weights, which may be viewed a categorified analogue of Racah-Wigner 6j-symbols. These weights solve a hexagon equation that encodes the formal invariance of the state sum under the Pachner moves of the triangulation. This result unravels the combinatorial formulation of the Feynman amplitudes of quantum field theory on flat spacetime proposed in A. Baratin and L. Freidel [Classical Quantum Gravity 24, 2027–2060 (2007)] which was shown to lead after gauge-fixing to Korepanov’s invariant of 4-manifolds.
A 2-categorical state sum model
NASA Astrophysics Data System (ADS)
Baratin, Aristide; Freidel, Laurent
2015-01-01
It has long been argued that higher categories provide the proper algebraic structure underlying state sum invariants of 4-manifolds. This idea has been refined recently, by proposing to use 2-groups and their representations as specific examples of 2-categories. The challenge has been to make these proposals fully explicit. Here, we give a concrete realization of this program. Building upon our earlier work with Baez and Wise on the representation theory of 2-groups, we construct a four-dimensional state sum model based on a categorified version of the Euclidean group. We define and explicitly compute the simplex weights, which may be viewed a categorified analogue of Racah-Wigner 6j-symbols. These weights solve a hexagon equation that encodes the formal invariance of the state sum under the Pachner moves of the triangulation. This result unravels the combinatorial formulation of the Feynman amplitudes of quantum field theory on flat spacetime proposed in A. Baratin and L. Freidel [Classical Quantum Gravity 24, 2027-2060 (2007)] which was shown to lead after gauge-fixing to Korepanov's invariant of 4-manifolds.
Sum Product Networks for Activity Recognition.
Amer, Mohamed R; Todorovic, Sinisa
2016-04-01
This paper addresses detection and localization of human activities in videos. We focus on activities that may have variable spatiotemporal arrangements of parts, and numbers of actors. Such activities are represented by a sum-product network (SPN). A product node in SPN represents a particular arrangement of parts, and a sum node represents alternative arrangements. The sums and products are hierarchically organized, and grounded onto space-time windows covering the video. The windows provide evidence about the activity classes based on the Counting Grid (CG) model of visual words. This evidence is propagated bottom-up and top-down to parse the SPN graph for the explanation of the video. The node connectivity and model parameters of SPN and CG are jointly learned under two settings, weakly supervised, and supervised. For evaluation, we use our new Volleyball dataset, along with the benchmark datasets VIRAT, UT-Interactions, KTH, and TRECVID MED 2011. Our video classification and activity localization are superior to those of the state of the art on these datasets.
Mo, Xiaobin; Yakiwchuk, Joshua; Dansereau, Julien; McCubbin, J Adam; Hall, Dennis G
2015-08-05
The development of general and more atom-economical catalytic processes for Friedel-Crafts alkylations of unactivated arenes is an important objective of interest for the production of pharmaceuticals and commodity chemicals. Ferroceniumboronic acid hexafluoroantimonate salt (1) was identified as a superior air- and moisture-tolerant catalyst for direct Friedel-Crafts alkylations of a variety of slightly activated and neutral arenes with stable and readily available primary and secondary benzylic alcohols. Compared to the use of classical metal-catalyzed alkylations with toxic benzylic halides, this methodology employs exceptionally mild conditions to provide a wide variety of unsymmetrical diarylmethanes and other 1,1-diarylalkane products in high yield with good to high regioselectivity. The optimal method, using the bench-stable ferroceniumboronic acid salt 1 in hexafluoroisopropanol as cosolvent, displays a broader scope compared to previously reported catalysts for similar Friedel-Crafts reactions of benzylic alcohols, including other boronic acids such as 2,3,4,5-tetrafluorophenylboronic acid. The efficacy of the new boronic acid catalyst was confirmed by its ability to activate primary benzylic alcohols functionalized with destabilizing electron-withdrawing groups like halides, carboxyesters, and nitro substituents. Arene benzylation was demonstrated on a gram scale at up to 1 M concentration with catalyst recovery. Mechanistic studies point toward the importance of the ionic nature of the catalyst and suggest that factors other than the Lewis acidity (pKa) of the boronic acid are at play. A SN1 mechanism is proposed where ion exchange within the initial boronate anion affords a more reactive carbocation paired with the non-nucleophilic hexafluoroantimonate counteranion.
Dou, Jian; Zeng, Hua Chun
2012-10-03
Herein we report an inside-out preinstallation-infusion-hydration method for targeted synthesis of Keggin heteropoly acids (silicomolybdic acid, H(4)SiMo(12)O(40)) within mesoporous silica (SiO(2)) hollow spheres. In this process, discrete molybdenum dioxide (MoO(2)) nanoparticles with diameter size ranging from 25 to 60 nm were first prepared by a one-pot hydrothermal route in water/ethanol mixed solvents at 180 °C, which were then used as cores to grow the shell of supramolecular templated silica with tetraethyl orthosilicate (TEOS) and hexadecyltrimethyl- ammonium chloride (CTACl) in alkaline solution. By thermal treatment of as-synthesized MoO(2)@SiO(2) core-shell spheres, the organic template was burned off and mesoporous shell was formed (BET specific surface area was as high as 872 m(2)/g). Meanwhile, the encapsulated MoO(2) was oxidized to Mo(6+) and infused to the mesoporous silica shells, forming heptamolybdate species (Mo(7)O(24)(6-)) uniformly dispersed on the mesopore surfaces of silica, while generating void space at the center of spheres. After hydration with water, H(4)SiMo(12)O(40) was formed by reaction between the surface Mo(7)O(24)(6-) and silica species in the presence of water. The prepared H(4)SiMo(12)O(40) @mSiO(2) hollow spheres were tested for Friedel-Crafts alkylation of toluene by benzyl alcohol. The H(4)SiMo(12)O(40)@mSiO(2) catalysts fabricated via this novel route exhibited excellent catalytic activity toward benzylation of toluene, which was approximately 2.6 times as high as that of commercial Amberlyst-15 catalyst. In addition, the H(4)SiMo(12)O(40)@mSiO(2) catalyst was very robust and could be reused after regeneration.
Zhu, Neng-Xiu; Zhao, Chao-Wei; Wang, Jian-Cheng; Li, Yan-An; Dong, Yu-Bin
2016-10-20
We report a convenient approach, the first of its kind, to construct a microscale non-metal@MOF composite catalytic host-guest system for an organic tandem reaction. The reported porous Cu4I4-MOF is able to reversibly adsorb molecular iodine at room temperature. The obtained I2@Cu4I4-MOF host-guest system can be a highly heterogeneous catalyst to promote the Friedel-Crafts alkylation of indoles with acetals in a one-pot two-step fashion under solvent-free conditions at room temperature.
García-García, Carolina; Ortiz-Rojano, Laura; Álvarez, Susana; Álvarez, Rosana; Ribagorda, María; Carreño, M Carmen
2016-05-06
Lewis acid catalyzed Friedel-Crafts alkylation of indoles has been achieved in high yields and selectivities using p-quinols as electrophiles. (S)-Binol-3,3'-(9-anthracenyl)-phosphoric acid was able to catalyze the enantioselective formation of 5-(3-indole)-2-cyclohexenone derivatives. Experimental results and theoretical calculations explained the enantioselectivity based on a transition state where two water molecules act as a tether joining the p-quinol with the phosphoric acid and the NH of indole, thus facilitating the desymmetrization of the prochiral cyclohexadienone framework.
Borthakur, Upasana; Borah, Madhurjya; Deka, Manash J; Saikia, Anil K
2016-10-07
A convenient protocol has been established for the synthesis of 1-tosyl-2,3,4,5-tetrahydro-1H-indeno[1,2-b]pyridine via cascade cyclization and Friedel-Crafts reaction of 4-methyl-N-(pent-4-yn-1-yl)benzenesulfonamides and aldehydes in good yields. The methodology has been used for the total synthesis of the antidepressant agent (±)-5-phenyl-2,3,4,4a,5,9b-hexahydro-1H-indeno[1,2-b]pyridine.
Suzuki, Yuta; Tanaka, Yuito; Nakano, Shun-ichi; Dodo, Kosuke; Yoda, Natsumi; Shinohara, Ken-Ichi; Kita, Kazuko; Kaneda, Atsushi; Sodeoka, Mikiko; Hamada, Yasumasa; Nemoto, Tetsuhiro
2016-03-18
A novel platinum-catalyzed cascade cyclization reaction was developed by intramolecular Friedel-Crafts-type C-H coupling of aniline derivatives with a propargyl carbonate unit-allylic amination sequence. Treatment of various propargyl carbonates tethered to meta-aniline derivatives with a Pt(dba)3/DPEphos catalyst system afforded the corresponding 3,4-fused tricyclic 3-alkylidene indolines in 42-99% yield, which were transformed into 3,4-fused indole derivatives by reaction with trifluoroacetic acid. The reaction products exhibited antiproliferative activities against cancer cells, but not normal cells, revealing the potential usefulness of this reaction for medicinal chemistry.
Chen, Yen-Bo; Liu, Shi-Hao; Hsieh, Min-Tsang; Chang, Chih-Shiang; Lin, Chun-Hung; Chen, Chen-Yin; Chen, Po-Yen; Lin, Hui-Chang
2016-04-01
Spiro bis-C,C-α-arylglycosides were synthesized in three steps in 78-85% overall yields starting from exo-glycals. The initial Heck type C-aryl addition of exo-glycals with arylboronic acids afforded α-aryl-β-substituted C-glycosides with exclusive α-stereoselectivity. Among the products, β-ethanal α-aryl C-glycosides further reacted with alkylthiol in the presence of InCl3, followed by in situ Friedel-Crafts cyclization to yield the desirable final products. We proposed a mechanism to explain how the α-aryl group serves as a main determinant of the cyclization.
Wu, Bin; Chopra, Rena; Yoshikai, Naohiko
2015-11-20
A one-pot multicomponent synthesis of a benzo[b]phosphole derivative has been achieved by a sequence of transition-metal-catalyzed arylmagnesiation of an internal alkyne, electrophilic trapping of the resulting alkenylmagnesium species with a dichloroorganophosphine, and an intramolecular phospha-Friedel-Crafts reaction. With appropriate arylmagnesiation and P-C bond formation conditions, the present method allows for the modular and expedient preparation of benzophospholes bearing a variety of substituents on the phosphorus atom, the C2 and C3 atoms, and the "benzo" moiety.
Kim, Hun Young; Song, Eunsun; Oh, Kyungsoo
2017-01-20
A facile synthetic method to chromenones and thiochromenones has been developed using a one-pot Friedel-Crafts acylation of alkynes with suitably substituted benzoyl chlorides. This unified approach to (thio)chromenones is readily applicable to aryl- and alkylalkynes where the stereochemically well-defined β-chlorovinyl ketone intermediates undergo distinctively different cyclization pathways. The ready availability of both starting materials, alkynes and benzoyl chlorides, coupled with the experimental simplicity makes the current synthetic method to (thio)chromenones fast, efficient, and practical.
NASA Astrophysics Data System (ADS)
Wu, Jiancheng; Cai, Hualun; Xu, Kai; Fu, Zien; Liu, Xin; Chen, Mingcai; Zhang, Xiuju
2012-11-01
The functionalization of carbon nanofibers (CNFs) with oxalyl chloride, via Friedel-Crafts reaction in the presence of aluminum chloride, was first demonstrated as an efficient way to introduce carboxyl groups onto the nanofiber sidewalls. Octa-aminophenylsilsesquioxane (OASQ) was then covalently attached to the carboxylated nanocarbon CNF-(COOH)n through amide linkage. Taking into account the nature of the electrophilic aromatic substitution, this chemical functionalization may involve formation of conjugated carboxylic acid moiety. Structural analysis combined with electron microscopy observation of the robust octasilsesquioxane species show that carboxyl groups are uniformly distributed on the nanofibers surface.
Simpson, E.J.; Koros, W.J.; Schechter, R.S.
1996-12-01
The performance of Friedel-Crafts modified polystyrene (FCMPS) as a volatile organic compound (VOC) sorbent is compared with commercially available polymers and activated carbon. Detailed analyses of the equilibrium isotherms are presented, including vapor phase isotherm temperature dependence and isosteric heats of sorption. Although significant absorption contributions are observed for the polymeric sorbents of this study, the data are mathematically well represented by Polanyi potential analysis. FCMPS can be synthesized with desirable performance qualities such as ultimate VOC sorption capacity of {approximately}2 mL/g, competitively high capacity in dilute streams versus activated carbon, insensitivity to humidity in vapor phase applications, and comparative ease of regeneration.
Dighe, Shashikant U; Yadav, Veena D; Mahar, Rohit; Shukla, Sanjeev K; Batra, Sanjay
2016-12-02
A triple cooperative catalysis-mediated multicomponent reaction between 1-formyl-N-substituted-β-carbolines, a terminal alkyne, and a secondary amine allows access to unprecedented polycyclic β-carbolines via sequential A(3)-coupling and an intramolecular Csp(2)-Csp(2) Friedel-Crafts arylation reaction. The reaction is successful in a dry inert atmosphere only with substrates bearing a methoxy-substituted benzyl group at the indole nitrogen. Conversely, treating 3-aminoindolizino[8,7-b]indoles (obtained after A(3)-coupling) with acid in the presence of H2O in air offers a general route to natural-alkaloid-like products.
Suzuki, Naoto; Fujita, Takeshi; Ichikawa, Junji
2015-10-16
Dibenzo[g,p]chrysenes were readily synthesized via the superacid- or TiF4-mediated domino Friedel-Crafts-type cyclization of 1,1-difluoroethenes bearing two biaryl groups, which were easily prepared via the Suzuki-Miyaura coupling of 1,1-difluoro-2,2-diiodoethene or 1-(biphenyl-2-yl)-1-bromo-2,2-difluoroethene. Using this approach, the activation of both vinylic and aromatic C-F bonds was successfully achieved to make new C-C bonds.
Reddy, B V Subba; Reddy, Y Vikram; Singarapu, Kiran Kumar
2016-01-21
2-Furylcarbinols undergo a smooth aza-Piancatelli rearrangement followed by Friedel-Crafts alkylation with a bifunctional substrate, (1H-pyrrol-1-yl)aniline, in the presence of 10 mol% In(OTf)3 in acetonitrile at room temperature to afford the corresponding hexahydrobenzo[b]cyclopenta[f]pyrrolo[1,2-d][1,4]diazepin-11(4aH)-one scaffolds in good yields. This method offers significant advantages such as high conversions, mild reaction conditions, short reaction times, and high selectivity. The relative stereochemistry of the product was established by nOe studies.
Ruengsangtongkul, S; Taprasert, P; Sirion, U; Jaratjaroonphong, J
2016-09-28
The FeCl3·6H2O-catalyzed three-component aza-Friedel-Crafts reaction of aromatic/heteroaromatic compounds, aromatic aldehydes and tert-butyl carbamate was reported. The subsequent Friedel-Crafts-type alkylation of the resulting tert-butyl diarylmethyl carbamate with heteroaromatic compounds under "open-flask" at room temperature was also performed. The two-step reaction was especially useful for the synthesis of functionalized nonsymmetrical heteroaryl-substituted triarylmethanes in good yields under an air atmosphere at room temperature.
ERIC Educational Resources Information Center
Laupa, Marta; Becker, Joe
2004-01-01
Arithmetic algorithms include two types of rules: conventional rules that may be changed by authority, and may legitimately vary from one classroom or country to another (e.g. putting the sum below, rather than above, the numbers added) and logical rules that involve the logic of the algorithm. Changes in the logical rules produce incorrect…
ERIC Educational Resources Information Center
Onorato, P.
2011-01-01
An introduction to quantum mechanics based on the sum-over-paths (SOP) method originated by Richard P. Feynman and developed by E. F. Taylor and coworkers is presented. The Einstein-Brillouin-Keller (EBK) semiclassical quantization rules are obtained following the SOP approach for bounded systems, and a general approach to the calculation of…
ERIC Educational Resources Information Center
Onorato, P.
2011-01-01
An introduction to quantum mechanics based on the sum-over-paths (SOP) method originated by Richard P. Feynman and developed by E. F. Taylor and coworkers is presented. The Einstein-Brillouin-Keller (EBK) semiclassical quantization rules are obtained following the SOP approach for bounded systems, and a general approach to the calculation of…
Some properties of the sum C1(h, k)
NASA Astrophysics Data System (ADS)
Cetin, Elif
2017-07-01
In [10], we have investigated properties of the sum C1(h, k). In this paper, we will give some other arithmetic properties of the sum C1(h, k). Moreover, in the light of the sum B1(h, k), which has also defined in [10], we will give specific values of the sum C1(h, k) when h + k is an odd number. Finally, we will give a relation between the sum C1(h, k) and the Hardy-Berndt sum s5(h, k) for a special case.
Partial Row-Sums of Pascal's Triangle
ERIC Educational Resources Information Center
Ollerton, Richard L.
2007-01-01
Identities for many and varied combinations of binomial coefficients abound. Indeed, because of the wide range of interrelationships it is possible that a great deal of mathematical effort has been wasted in proving essentially equivalent formulae. As well as proving identities these methods can be used to rule out closed form solutions (at least…
Partial Row-Sums of Pascal's Triangle
ERIC Educational Resources Information Center
Ollerton, Richard L.
2007-01-01
Identities for many and varied combinations of binomial coefficients abound. Indeed, because of the wide range of interrelationships it is possible that a great deal of mathematical effort has been wasted in proving essentially equivalent formulae. As well as proving identities these methods can be used to rule out closed form solutions (at least…
Sum-SINR/sum-capacity optimal multisignature spread-spectrum steganography
NASA Astrophysics Data System (ADS)
Wei, Lili; Pados, Dimitris A.; Batalama, Stella N.; Medley, Michael J.
2008-04-01
For any given digital host image or audio file (or group of hosts) and any (block) transform domain of interest, we find an orthogonal set of signatures that achieves maximum sum-signal-to-interference-plus-noise ratio (sum- SINR) spread-spectrum message embedding for any fixed embedding amplitude values. We also find the sumcapacity optimal amplitude allocation scheme for any given total distortion budget under the assumption of (colored) Gaussian transform-domain host data. The practical implication of the results is sum-SINR, sumcapacity optimal multiuser/multisignature spread-spectrum data hiding in the same medium. Theoretically, the findings establish optimality of the recently presented Gkizeli-Pados-Medley multisignature eigen-design algorithm.
Evans, Philip; Wolf, Bob
2005-01-01
Corporate leaders seeking to boost growth, learning, and innovation may find the answer in a surprising place: the Linux open-source software community. Linux is developed by an essentially volunteer, self-organizing community of thousands of programmers. Most leaders would sell their grandmothers for workforces that collaborate as efficiently, frictionlessly, and creatively as the self-styled Linux hackers. But Linux is software, and software is hardly a model for mainstream business. The authors have, nonetheless, found surprising parallels between the anarchistic, caffeinated, hirsute world of Linux hackers and the disciplined, tea-sipping, clean-cut world of Toyota engineering. Specifically, Toyota and Linux operate by rules that blend the self-organizing advantages of markets with the low transaction costs of hierarchies. In place of markets' cash and contracts and hierarchies' authority are rules about how individuals and groups work together (with rigorous discipline); how they communicate (widely and with granularity); and how leaders guide them toward a common goal (through example). Those rules, augmented by simple communication technologies and a lack of legal barriers to sharing information, create rich common knowledge, the ability to organize teams modularly, extraordinary motivation, and high levels of trust, which radically lowers transaction costs. Low transaction costs, in turn, make it profitable for organizations to perform more and smaller transactions--and so increase the pace and flexibility typical of high-performance organizations. Once the system achieves critical mass, it feeds on itself. The larger the system, the more broadly shared the knowledge, language, and work style. The greater individuals' reputational capital, the louder the applause and the stronger the motivation. The success of Linux is evidence of the power of that virtuous circle. Toyota's success is evidence that it is also powerful in conventional companies.
Simple pulse counting circuit computes sum of squares
NASA Technical Reports Server (NTRS)
Schaefer, D. H.
1965-01-01
Pulse counting circuit with an extra chain of flip-flops, delay lines, and gates computes the sum of the squares of the pulse sequences. A pulse train and the sum of the squares of the pulses are simultaneously completed.
20 CFR 225.26 - Residual Lump-Sum PIA.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 20 Employees' Benefits 1 2010-04-01 2010-04-01 false Residual Lump-Sum PIA. 225.26 Section 225.26... INSURANCE AMOUNT DETERMINATIONS PIA's Used in Computing Survivor Annuities and the Amount of the Residual Lump-Sum Payable § 225.26 Residual Lump-Sum PIA. The Residual Lump-Sum PIA (RLS PIA) is used to compute...
Boiaryna, Liliana; Azizi, Mohamed Salah; El Bouakher, Abderrahman; Picard, Baptiste; Taillier, Catherine; Othman, Mohamed; Trabelsi-Ayadi, Malika; Dalla, Vincent
2015-05-01
The combined use of Tf2NH and L(Au)(+)X(-) as a dual or binary catalytic system clearly improves the efficiency and enlarges the scope of the tandem intermolecular Friedel-Crafts α-amidoalkylation/intramolecular hydroarylation sequence, compared to an "all gold" multicatalysis approach.
Wu, Shanchao; Liu, Na; Dong, Guoqiang; Ma, Lin; Wang, Shengzheng; Shi, Wencai; Fang, Kun; Chen, Shuqiang; Li, Jian; Zhang, Wannian; Sheng, Chunquan; Wang, Wei
2016-07-21
An efficient redox-amination-aromatization-Friedel-Crafts acylation cascade process from trans-4-hydroxyproline and 2-formylbenzoic acids has been developed for the synthesis of pyrrolo[1,2-b]isoquinolin-10(5H)-ones. Compound 3h was identified as a new potent dual topoisomerase I/II inhibitor.
22 CFR 19.13-1 - Lump-sum credit.
Code of Federal Regulations, 2011 CFR
2011-04-01
... 22 Foreign Relations 1 2011-04-01 2011-04-01 false Lump-sum credit. 19.13-1 Section 19.13-1... THE FOREIGN SERVICE RETIREMENT AND DISABILITY SYSTEM § 19.13-1 Lump-sum credit. “Lump-sum credit” is the compulsory and special contributions to a participant's or former participant's credit in the...
29 CFR 4050.8 - Automatic lump sum.
Code of Federal Regulations, 2010 CFR
2010-07-01
... determined under § 4050.5(a)(1) (mandatory lump sum) or § 4050.5(a)(2) (de minimis lump sum). (a) General... the deemed distribution date, to the missing participant's estate. (b) De minimis annuity alternative... under § 4050.5(a)(2) (de minimis lump sum) (or the guaranteed benefit form for a beneficiary of such...
29 CFR 4050.8 - Automatic lump sum.
Code of Federal Regulations, 2012 CFR
2012-07-01
... determined under § 4050.5(a)(1) (mandatory lump sum) or § 4050.5(a)(2) (de minimis lump sum). (a) General... the deemed distribution date, to the missing participant's estate. (b) De minimis annuity alternative... under § 4050.5(a)(2) (de minimis lump sum) (or the guaranteed benefit form for a beneficiary of such...
27 CFR 24.148 - Penal sums of bonds.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Penal sums of bonds. 24.148 Section 24.148 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU... Penal sums of bonds. The penal sums of bonds prescribed in this part are as follows: Bond Basis Penal...
22 CFR 19.13-1 - Lump-sum credit.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 22 Foreign Relations 1 2010-04-01 2010-04-01 false Lump-sum credit. 19.13-1 Section 19.13-1... THE FOREIGN SERVICE RETIREMENT AND DISABILITY SYSTEM § 19.13-1 Lump-sum credit. “Lump-sum credit” is the compulsory and special contributions to a participant's or former participant's credit in the Fund...
Rates of profit as correlated sums of random variables
NASA Astrophysics Data System (ADS)
Greenblatt, R. E.
2013-10-01
Profit realization is the dominant feature of market-based economic systems, determining their dynamics to a large extent. Rather than attaining an equilibrium, profit rates vary widely across firms, and the variation persists over time. Differing definitions of profit result in differing empirical distributions. To study the statistical properties of profit rates, I used data from a publicly available database for the US Economy for 2009-2010 (Risk Management Association). For each of three profit rate measures, the sample space consists of 771 points. Each point represents aggregate data from a small number of US manufacturing firms of similar size and type (NAICS code of principal product). When comparing the empirical distributions of profit rates, significant ‘heavy tails’ were observed, corresponding principally to a number of firms with larger profit rates than would be expected from simple models. An apparently novel correlated sum of random variables statistical model was used to model the data. In the case of operating and net profit rates, a number of firms show negative profits (losses), ruling out simple gamma or lognormal distributions as complete models for these data.
40 CFR 90.708 - Cumulative Sum (CumSum) procedure.
Code of Federal Regulations, 2014 CFR
2014-07-01
... applicable, the manufacturer's final credit report as required by § 90.210 must break out the credits that... limit for two consecutive tests. Where applicable, the manufacturer's final credit report as required by § 90.210 must break out the credits that result from each FEL and corresponding CumSum analysis for the...
40 CFR 90.708 - Cumulative Sum (CumSum) procedure.
Code of Federal Regulations, 2011 CFR
2011-07-01
... applicable, the manufacturer's final credit report as required by § 90.210 must break out the credits that... limit for two consecutive tests. Where applicable, the manufacturer's final credit report as required by § 90.210 must break out the credits that result from each FEL and corresponding CumSum analysis for the...