Distribution of valence quarks in hadrons in QCD: theoretical method of calculations

Abstract

The general method for calculation of valence quark distributions in hadrons at intermediate $x$ is presented. The imaginary part of virtual photon forward scattering amplitude on quark current with hadron quantum number is considered in the case, when initial and final virtualities of the current $p^2_1$ and $p^2_2$ are different, negative and large: $\mid p^2_1\mid, \mid p^2_2\mid\gg R^{-2}_c$, where $R_c$ is confinement radius. The operator product expansion (OPE) in $p^2_1,p^2_2$ up to dimension 6 operators is performed. Double dispersion representations in $p^2_1, p^2_2$ of the amplitude in terms of physical states contributions are used. Equalling them to those calculated in QCD by OPE the desired sum rules for quark distributions in mesons are found. The double Borel transformations are applied to the sum rules, killing non-diagonal transition terms, which deteriorated the accuracy in the previous calculations of quark distributions in nucleon. Leading order perturbative corrections are accounted. Valence quark distributions in pion, longitudinally and transversally polarized $\rho$-mesons and proton are calculated at intermediate $x$, $0.2 \la x \la 0.7$ and normalization points $Q^2 = 2-5 \~GeV^2$ with no fitting parameters. In cases of pion and proton the results are in agreement with found correspondingly from the data on the Drell-Yan process and deep inelastic scattering. Valence quark distributions in transversally and longitudinally polarized $\rho$-mesons are essentially different one from another and also differ from those in pion.