Quark Distribution in Pion within Instanton Liquid Model

TL;DR

This paper calculates the valence-quark distribution in the pion using the instanton liquid model, deriving an analytic expression, and compares the evolved results with experimental data, showing good agreement.

Contribution

It introduces a gauge-invariant framework within the instanton liquid model to derive the pion's quark distribution function analytically.

Findings

Derived an analytic expression for the pion's quark distribution function.

QCD evolution of the distribution aligns well with experimental data.

Connected instanton parameters to vacuum condensates and pion observables.

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.