Gottfried sum rule from maximum entropy method quark distributions with DGLAP evolution and with DGLAP evolution with GLR-MQ-ZRS corrections

A new method to test the valence quark distribution of nucleons obtained from the maximum entropy method using the Gottfried sum rule by performing the DGLAP equations with GLR-MQ-ZRS corrections and the original leading-order/next-to-leading-order(LO/NLO) DGLAP equations is outlined. The test relies on knowledge of the unpolarized electron–proton structure function F_2~(ep) and the electron–neutron structure function F_2~(en) and the assumption that Bjorken scaling is satisfied. In this work, the original Gottfried summation value obtained by the integrals of the structure function at different Q~2 is in accordance with the theoretical value of 1/3 under the premise of light-quark flavor symmetry of the nucleon sea, whether it results from dynamical evolution equations or from global quantum chromodynamics fits of PDFs. Finally, we present the summation value of the LO/NLO DGLAP global fits of PDFs under the premise of light-quark flavor asymmetry of the nucleon sea. According to analysis of the original Gottfried summation value with two evolution equations at different Q~2, we find that the valence quark distributions of nucleons obtained by using the maximum entropy method are effective and reliable.     

A comprehensive revisit of the ρ meson with improved Monte-Carlo based QCD sum rules

We improve the Monte-Carlo based QCD sum rules by introducing the rigorous H¨older-inequalitydetermined 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.     

Improved calculations of quark distributions in hadrons: the case of the pion

The earlier introduced method of calculation of quark distributions in hadrons, based on QCD sum rules, is improved. The imaginary part of the virtual photon forward scattering amplitude on some hadronic current is considered in the case, when initial and final virtualities of the current , and are different, . The operator product expansion (OPE) in , is performed. The sum rule for quark distribution is obtained using double dispersion representation of the amplitude on one side in terms of calculated in QCD OPE and on the other side in terms of physical states contributions. Double Borel transformation in , is applied to the sum rule, killing background non-diagonal transition terms which deteriorated the accuracy in previous calculations. The case of the valence quark distribution in the pion is considered, which was impossible to treat by the previous method. OPE up to dimension 6 operators is performed and leading order perturbative corrections are accounted. Valence u-quark distribution in was found at intermediate x, , and normalization point . These results may be used as input for evolution equations. Received: 14 July 1999 / Published online: 6 March 2000     

Coupled QCD sum rules for positive and negative-parity nucleons

A new approach of the QCD sum rule is proposed in which positive and negative-parity baryons couple with each other. With positive and negative-parity states explicitly taken into account, sum rules are derived by means of the dispersion relation in energy. The method is applied to the nucleon channel and the parity splitting of the nucleon resonance states is studied. It is found that the obtained sum rules have a very good Borel stability. This suggests that the ansatz for the spectral function in the present sum rule approximates the physical spectrum better than the usual lowest pole plus continuum ansatz. The predicted masses of the positive and negative nucleons reproduce the experimental ones fairly well. Especially, the mass difference is extremely close to the experimental value.     

Quarkonia at Finite T: An Approach Based On QCD Sum Rules and the Maximum Entropy Method

Quarkonium spectral functions at finite temperature are studied, making use of a recently developed method of analyzing QCD sum rules by the maximum entropy method. This approach enables us to directly obtain the spectral function from the sum rules, without having to introduce any specific assumption about its functional form. QCD sum rules for heavy quarkonia incorporate finite temperature effects in form of changing values of the various gluonic condensates that appear in the operator product expansion. These changes depend on the energy density and pressure at finite temperature, which we extract from quenched lattice QCD calculations. As a result, it is found that the charmonium ground states of both S-wave and P-wave channels dissolve into the continuum already at temperatures around or slightly above the critical temperature T _c , while the bottomonium states are less influenced by temperature effects, surviving up to about 2.5 T _c or higher for S-wave and about 2.0 T _c for P-wave states.     

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.     

Dispersive methods and QCD sum rules for γ γ collisions

It has been shown, in the case of meson photoproduction, that the power-law falloff of these reactions can be described by lowest-order (real) sum rules, at moderate momentum transfer. The phases of these processes, in this regime, are usually thought to be non-perturbative. In a sum rule framework, however, they can possibly be described by radiative corrections to the hadronic spectral densities of the corresponding helicities, which become complex functions to order α_s, and the effects of interference can be strongly enhanced by the presence of the vacuum condensates in the dispersion relation. It is shown that the imaginary parts of these complex corrections have a factorized form and can be evaluated in a systematic fashion, while their real parts, at the same perturbative order, are down by at least two powers of momentum transfer. The analysis is done at two-loop level, combining dimensional regularization and light-cone methods. The calculations are performed for all the independent set of scalar diagrams generated by the OPE. The analytical bounds are identified and discussed.     

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.     

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.     

A computation of Adler's β sum rule II

We improve our previous calculation of Adler's β sum rule by including the Born contributions to the πN states. The result is that the sum rule is only balanced if the weak axial nucleon form factor g_A(q²) and the strong pion-nucleon form factor have roughly the same q² dependance.     

A K-harmonics description of 16O breathing mode

We calculate the properties of the ¹⁶O breathing mode in a K_minK-harmonics calculation. The breathing mode has single particle quantum numbers that are identical to the nucleon quantum numbers in the ground state. We calculate an excitation energy of 27 MeV, and a monopole transition matrix element of 7.21 fm². Six excited monopole states are calculated to be bound in ¹⁶O, with k equal to K_min. These states exhaust 90 % of the isoscalar monopole sum rule. The first excited K_min state, the breathing mode, exhausts 68 % of the isoscalar sum rule.     

Instanton interpolating current for σ-tetraquark

We perform a QCD sum rule analysis for the light scalar meson σ   (f₀(600)$f_0(600)$) with a tetraquark current related to the instanton picture for QCD vacuum. We demonstrate that instanton current, including equal weights of scalar and pseudoscalar diquark–antidiquarks, leads to a strong cancelation between the contributions of high dimension operators in the operator product expansion (OPE). Furthermore, in the case of this current direct instanton contributions do not spoil the sum rules. Our calculation, obtained from the OPE up to dimension 10 operators, gives the mass of σ-meson around 780 MeV.     

The Fubini-Furlan-Rossetti sum rule revisited

The Fubini-Furlan-Rossetti sum rule for pion photoproduction on the nucleon is evaluated by dispersion relations at constant t, and the corrections to the sum rule due to the finite pion mass are calculated. Near threshold these corrections turn out to be large due to pion-loop effects, whereas the sum rule value is closely approached if the dispersion integrals are evaluated for sub-threshold kinematics. This extension to the unphysical region provides a unique framework to determine the low-energy constants of chiral perturbation theory by global properties of the excitation spectrum.     

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.     

Memorino on the ‘1/2 versus 3/2 puzzle’ in B̄→lν̄X<Subscript>c</Subscript> – a year later and a bit wiser

The OPE treatment that has been so successful in describing inclusive B̄→lν̄X_c decays yields sum rules (in particular the Uraltsev sum rule and its higher moments) implying the dominance of the P wave j_q=3/2 charm states in X_c over their j_q=1/2 counterparts. This prediction is supported by other general arguments as well as quark model calculations, which illustrate the OPE results, and by preliminary lattice findings. Its failure would indicate a significant limitation in our theoretical understanding of B̄→lν̄X_c. Some experimental issues have been clarified since a preliminary version of this note had appeared; yet, the verdict on the composition of the final states beyond D, D^* and the two narrow j_q=3/2 resonances remains unsettled. Establishing which hadronic configurations – D/D^*+π,D/D^*+2π,... – contribute, what their quantum numbers are, and their mass distributions will require considerable experimental effort. We explain the theoretical issues involved and why a better understanding of them will be of considerable value. Having significant contributions from a mass continuum distribution below 2.5 GeV raises serious theoretical questions for which we have no good answer. Two lists are given, one with measurements that need to be done and one with items of theoretical homework. Some of the latter can be done by employing existing theoretical tools, whereas others need new ideas.     

Nucleon propagator at finite temperature

We study the nucleon propagator at finite temperature in the framework of finite energy QCD sum rules. We find that the nucleon mass is approximately constant over a wide range of temperature, increasing sharply near the critical temperature for deconfinementT _c . The coupling of the nucleon to quarks is a monotonically decreasing function ofT, vanishing atT=T _c .     

Diquarks in nucleons

Under the assumption that a scalar diquark coexists in part of the time with a single quark within a nucleon, which is favored to describe the higher twist effects of both γ and ν induced nucleon structure functions consistently, we consider how its presence affects nucleon properties. It is shown that the sum rule and the magnetic moment constrain its contribution strongly and the asymmetry is quite sensitive to it. In particular, theR=σ _L /σ _T ratio can be explained in terms of the large transverse momentum of the diquark which arises from the consideration on the neutron charge radius value.     

Gottfried and Bjorken sum rules: The role of vector diquarks

A quark-diquark model of the nucleon is considered and the value of the Gottfried sum ruleS _G , recently measured by the NMC group and found to differ considerably from the quark parton model expectation,S _G =1/3, is computed allowing for both elastic and inelastic contributions from the diquarks. This approach fails to reproduce the data, unless vector diquark contributions persist at very largeQ ² values, contrary to the usual assumptions. The Bjorken sum rule andSU(6) violations due to the quark-diquark structure of the nucleon are also briefly discussed.     

The use of finite energy sum rules for the description of the hadronic properties of QCD

We use finite energy sum rules, taking into account nonperturbative corrections, for the calculation of hadron masses within QCD. As a rule, we obtain reasonable agreement with experimental data. We also estimate the proton lifetime in theSU(5) model to beτ _p =10²⁸ (M _x /10¹⁴GeV)⁴ years.     

Ground state baryon magnetic moments and nucleon axial vector coupling

Ground-state baryon magnetic moments and nucleon axial vector coupling are calculated usingqcd inspired configuration mixing and relativistic corrections. Unlike earlier attempts, we incorporate a natural mass scale for quarks, taken as one third the nucleon mass for up and down quarks, and the strange quark mass suggested by the Lipkin’s sum rule. In the parameter-free non-relativistic limit, we find a fairly good fit, which improves upon including relativistic corrections.