Parton-distribution functions for the pion and kaon in the gauge-invariant nonlocal chiral-quark model

TL;DR

This paper calculates the parton-distribution functions for pion and kaon using a gauge-invariant nonlocal chiral-quark model, incorporating momentum-dependent quark masses and evolving results to higher energy scales, with results aligning qualitatively with empirical data.

Contribution

It introduces a gauge-invariant nonlocal chiral-quark model that accurately accounts for vector current conservation and momentum dependence in PDFs of mesons, advancing previous models.

Findings

Nonlocal contributions account for about 30% of the PDF strength.

Model results show qualitative agreement with empirical data.

High-Q^2 evolution of PDFs aligns with experimental observations.

Abstract

We investigate the parton-distribution functions (PDFs) for the positively charged pion and kaon at a low-renormalization scale ~ 1 GeV. To this end, we employ the gauge-invariant effective chiral action from the nonlocal chiral-quark model, resulting in that the vector currents are conserved. All the model parameters are determined phenomenologically with the normalization condition for PDF and the empirical values for the pseudoscalar-meson weak-decay constants. We consider the momentum dependence of the effective quark mass properly within the model calculations. It turns out that the leading local contribution provides about 70 % of the total strength for PDF, whereas the nonlocal one that is newly taken into account in this work for the gauge invariance does the rest. High-Q^2 evolution to 27 GeV^2 is performed for valance-quark distribution function (VQDF), using the DGALP equation. The moments for the pion and kaon VQDFs are also computed. The numerical results are compared with the empirical data and theoretical estimations, and show qualitatively agreement with them.