Quark Distribution in Pion within Instanton Liquid Model

Abstract

The leading-twist valence-quark distribution function in the pion is obtained at a low normalization scale of an order of the inverse average size of an instanton $\rho_c$. The momentum dependent quark mass and the quark-pion vertex are constructed in the framework of the instanton liquid model, using a gauge invariant approach. The parameters of instanton vacuum, the effective instanton radius and quark mass, are related to the vacuum expectation values of the lowest dimension quark-gluon operators and to the pion low energy observables. An analytic expression for the quark distribution function in the pion for a general vertex function is derived. The results are QCD evolved to higher momentum-transfer values, and reasonable agreement with phenomenological analyzes of the data on parton distributions for the pion is found.