Hadronic quark distribution amplitudes from QCD sum-rule moments

We discuss the reliability of hadronic wave functions (quark distribution amplitudes) determined by a finite number of QCD sum-rule moments. Although the expansion coefficients for polynomial models of the wave function are uniquely determined by the moments, the inherent uncertainty in such moments leads to a considerable indeterminacy in the wave functions because minimal changes of the moments can lead to large oscillations of the model function. In particular, the freedom in the moments left by QCD sum rules leads to a nonconverging polynomial expansion. This remains true even if additional constraints on the wave functions are used. As a consequence of this, the widely used procedure of constructing polynomial models of hadronic wave function from QCD sum rule moments does not guarantee even a reasonable approximation to the true wave function. The differences among the model wave functions persist also in the calculations of physical observables like hadronic form factors. This implies that physical observables calculated by means of such model wave functions are in general very unreliable. As specific examples, we examine the pion and nucleon wave functions and show that Gegenbauer as well as Appell polynomial expansions constructed from QCD sum rule moments are ruled out. The implications for the wave functions which are generally used in the literature are discussed.     

New approach to axial coupling constants in the QCD sum rule

We derive new QCD sum rules for the axial coupling constants by considering the correlation functions of axial-vector currents in a one-nucleon state. The QCD sum rules tell us that the axial coupling constants are expressed by nucleon matrix elements of quark-gluon composite operators which are related to the sigma terms and the moments of parton distributions. The results for the isovector axial coupling constants and the eighth component of the SU(3)(f) octet are in good agreement with experiment.     

Charge and Current Sum Rules in Quantum Media Coupled to Radiation

This paper concerns the equilibrium bulk charge and current density correlation functions in quantum media, conductors and dielectrics, fully coupled to the radiation (the retarded regime). A sequence of static and time-dependent sum rules, which fix the values of certain moments of the charge and current density correlation functions, is obtained by using Rytov’s fluctuational electrodynamics. A technique is developed to extract the classical and purely quantum-mechanical parts of these sum rules. The sum rules are critically tested in the classical limit and on the jellium model. A comparison is made with microscopic approaches to systems of particles interacting through Coulomb forces only (the non-retarded regime). In contrast with microscopic results, the current-current density correlation function is found to be integrable in space, in both classical and quantum regimes.     

Observables for the even type of nucleon in the ground states of odd-mass nuclei

Existing data for lighter nuclei on observables, including magnetic moments and single particle multiple moments, are explained if the even nucleons are predominantly coupled to spin zero but with a substantial spin-2 wave function component. Strong predictions can be made on the basis of such wave functions regarding spectroscopic sum rules and the behaviour of general observables such as B(EL) transition rates.     

Spin Structure of Baryons in Orbiting Valence Quark Model

The quark model with orbital motion of the valence quarks is constructed to reproduce the spin structure of baryons. The relations between the spin-averaged sum rules and baryon magnetic moments found in the previous works do not remain, unless the small orbital magnetic moments are neglected. In particular, when the orbital motion of the valence quarks leads to the small contribution of quark orbit-spin to baryon magnetic moments, the sum rules for polarized nucleon are in agreement with the recent experiment.     

Moments of the heavy-quark parton distribution function from QCD sum rules

The moments of the heavy-quark parton distribution functions in a heavy pseudoscalar meson are calculated from QCD sum rules. Expanding these sum rules in the inverse heavy-quark mass we obtain the heavy-mass limits of the moments. Comparison with the finite-mass results reveals that while the heavy-mass expansion works reasonably well for the b quark, one has to take into account terms of higher order than (1/m _c )² for the c quark. This result can provide a quantitative assessment of c- and b-quark fragmentation models based on the heavy-quark mass limit. The text was submitted by the authors in English.     

Photo-absorption sum rules σ<Subscript>–1</Subscript> in different environments (Atoms,nuclei, nucleons)

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.     

New sum rules for polarized deep inelastic scattering

Relations between the structure functions g₁ and g₂ of polarized DIS are derived in the leading perturbative QCD approximation, starting with the sum rules for twist-3 parton correlation functions which follow from gauge invariance and the equation of motion of the quark fields. For the first moments they coincide with the approximate relations proposed earlier by Wandzura and Wilczek as well as Bukhvostov, Kuraev and Lipatov.     

OPE analysis of the nucleon scattering tensor: a review including weak interactions and finite mass effects

We perform a systematic operator product expansion of the most general form of the nucleon scattering tensorW _μν including electro-magnetic and weak interaction processes. Finite quark masses are taken into account and a number of higher-twist corrections are included. In this way we derive relations between the lowest moments of all 14 structure functions and matrix elements of local operators. Besides reproducing well-known results, new sum rules for parity-violating polarized structure functions and new mass correction terms are obtained.     

x-space sum rules and the pion wave function in QCD

From two-point correlators of (derivative) axial currents we construct sum rules in Euclidean configuraton space for the moments of the pion wave-function. Analysis of these sum rules gives a value of the second moment \(\left\langle {\xi ^2 } \right\rangle \) compatible with those obtained from conventional sum rules but in disagreement with that obtained in a recent lattice calculation.     

The ratios among condensates from e+e− (I=1) data

We calculate the ratios among condensates from the ρ channel (I=1) e⁺e⁻ data in a systematic way. We use quotients of SVZ sum rules for different moments of the correlation functions. The results turn out to be very accurate. A factor of 1.6 for the ratio of the four quark condensate over the gluon condensate compared with the standard value is predicted.     

Bound-state perturbation method via SVZ sum rules in quantum mechanics

The perturbation method for bound states within the framework of the Shifman-Vainshtein-Zakharov sum rule method is studied on simple systems (linear harmonic oscillator, hydrogen atom) in external electric fields. It is pointed out that for stronger fields reasonable results for the ground-state energy can only be achieved when sum rules are written for the correction to the Euclidean Green function caused by the external field. Moreover, if the system is bound by a singular (Coulomb) potential, one needs to sum higher perturbative corrections to the Green function and to find a realistic approximation of the continuum contribution to the sum rules. The results are of relevance e.g. for calculations of nucleon magnetic moments and toponium properties via SVZ sum rules in QCD.     

Some consequences of relativistic effects upon optical spectra

Large spin–orbit interaction produces large orbital magnetic moments in narrow energy bands. Since the orbital character of the wave functions is more important in orbital than in spin magnetism, the limitations of the local spin density approximation become evident. It is possible to keep the orbital dependence of the exchange interactions by using an orbital polarization scheme or by using Hartree–Fock theory with screened Slater integrals for exchange. This leads to an enhancement of the calculated orbital moment when the magnetism is strong. Recently calculated magnetic moments and calculated sum rules for X-ray magnetic circular dichroism in US are described. Received: 23 May 2001 / Accepted: 4 July 2001 / Published online: 5 October 2001     

Sum rules for nuclear collective excitations

Characterizations of the response function and of integral properties of the strength function via a moment expansion are discussed. Sum rule expressions for the moments in the RPA are derived. The validity of these sum rules for both density independent and density dependent interactions is proved. For forces of the Skyrme type, analytic expressions for the plus three energy weighted sum rules are given for isoscalar monopole and quadrupole operators. From these, a close relationship between the monopole and quadrupole energies is shown and their dependence on incompressibility and effective mass is studied. The inverse energy weighted sum rule is computed numerically for the monopole operator, and an upper bound for the width of the monopole resonance is given. Finally the reliability of moments given by the RPA with effective interactions is discussed using simple soluble models for the hamiltonian, and also by comparison with experimental data.     

Optical Properties of Model Moderately Coupled Plasmas

We review our approach to the modelling of optical properties of model moderately coupled plasmas. On the basis of the classical theory of moments the external and internal dynamic conductivities and the reflectivity coefficient of a model hydrogen moderately coupled plasma are determined using all known exact relations and sum rules. The sum rules which are the power frequency moments of the loss function are calculated using the Deutsch effective potential and the hypernetted chain equations. MD simulation data are used and numerical simulations are suggested (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Pump and probe nonlinear processes: new modified sum rules from a simple oscillator model

The nonlinear oscillator model is useful to basically understand the most important properties of nonlinear optical processes. It has been shown to give the correct asymptotic behaviour and to provide the general features of harmonic generation to all orders, in particular dispersion relations and sum rules. We investigate the properties of pump and probe processes using this model, and study those cases where general theorems based on the holomorphic character of the Kubo response functions cannot be applied. We show that it is possible to derive new sum rules and new Kramers-Kr?nig relations for the two lowest moments of the real and of the imaginary part of the third order susceptibility and that new specific contributions become relevant as the intensity of the probe increases. Since the analytic properties of the susceptibility functions depend only upon the time causality of the system we are confident that these results are not model dependent and therefore have a general validity, provided one substitutes for the equilibrium values of the potential derivatives the density matrix expectation values of the corresponding operators. Received 25 January 1999 and Received in final form 26 April 1999     

Valence shell calculations on polyatomic molecules

Molecular quadrupole moments were calculated for some diatomic, symmetric top and small planar molecules by CNDO/2D and SCC methods. The results resemble those obtained by ab initio minimal basis set calculations and give a fairly good agreement with experimental data. The latter are closely reproduced only by ab initio extended basis set calculations indicating that molecular quadrupoles provide a sensitive test of the quality of the molecular wave functions. Flygare's empirical additivity rules for out-of-plane second moments of electronic charge distribution were rationalized in terms of CNDO/2 MO's over orthogonal AO's. In this model only one-centre terms are important and the sum of one-centre terms was approximately constant for the first-row atoms.     

QCD sum rules in exclusive kinematics and pion wave function

We suggest a modification of the QCD sum rules for three-point correlation functions that relates hadron expectation values of an operator of interest to properties of the QCD vacuum in alternating external fields. A new sum rule is obtained for the nucleon magnetic moments. Relations are found between the couplings g_πNN , g_ρωπ and the value of the pion wave function at the point with equal momentum carried by the quark and the antiquark. Our results seem to exclude the possibility of having a pronounced dip in the pion wave function in the middle point, as has been assumed on the evidence of a large value of the second moment.