Improved calculations of quark distributions in hadrons: the case of the pion
B.L. Ioffe - A.G. Oganesian
Institute of Theoretical and Experimental Physics,
B.Cheremushkinskaya 25, 117218, Moscow, Russia
Received: 14 July 1999 / Published online: 6 March 2000 - © Springer-Verlag 2000
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 p21, and p22 are different, . The operator product expansion (OPE) in p21, p22 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 p21, p22 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, 0.15 < x < 0.7, and normalization point . These results may be used as input for evolution equations.
Copyright Società Italiana di Fisica, Springer-Verlag 2000