Valence quark distributions in mesons in generalized QCD sum rules

The method for calculation of valence quark distributions at intermediate x is presented. The imaginary part of the virtual photon forward scattering amplitude on the quark current with meson quantum number is considered. The initial and final virtualities p(1)(2) and p(2)(2) of the currents are assumed to be large, negative, and different, p(1)(2) not equal p(2)(2). The operator product expansion (OPE) in p(1)(2), p(2)(2) up to dimension 6 operators is performed. Double dispersion representations in p(1)(2), p(2)(2) of the amplitude in terms of physical state contributions are used. Setting them equal 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, destroying nondiagonal transition terms, which deteriorated the accuracy in the previous calculations of quark distributions in the nucleon. Leading-order perturbative corrections are taken into account. Valence quark distributions in the pion and longitudinally and transversally polarized rho mesons are calculated at intermediate x, 0.2 less than or equal tox less than or equal to0.7 and normalization points Q(2) = 2-4 GeV2 with no fitting parameters. The use of the Regge behavior at small x and quark counting rules at large x allows one to find the first and the second moments of valence quark distributions. The obtained quark distributions may be used as an input for evolution equations. In the case of the pion the quark distribution is in agreement with those found from the data on the Drell-Yan process. The quark distributions in transversally and longitudinally polarized rho mesons are essentially different.