An Analysis of Parton Distribution Functions of the Pion and the Kaon with the Maximum Entropy Input

TL;DR

This paper derives pion and kaon parton distribution functions using a maximum entropy input in a dynamical QCD framework, successfully matching experimental data and analyzing their asymptotic behaviors and moments.

Contribution

It introduces a novel approach using maximum entropy for the initial valence distributions in a dynamical QCD analysis of pion and kaon PDFs.

Findings

Valence and sea quark distributions agree with experimental data.

Asymptotic behaviors at small and large x are characterized.

First three moments of distributions are consistent with other theories.

Abstract

We present pion and kaon parton distribution functions from a global QCD analysis of the experimental data within the framework of dynamical parton model. We use the DGLAP equations with parton-parton recombination corrections and the valence input of uniform distribution which maximizes the information entropy. At our input scale $Q_0^2$, there are no sea quark and gluon distributions. All the sea quarks and gluons of the pion and the kaon are completely generated from the parton splitting processes. The mass-dependent parton splitting kernel is applied for the strange quark distribution in the kaon. The obtained valence quark and sea quark distributions at high $Q^{2}$ ($Q^2>5$ GeV$^2$) are compatible with the existed experimental measurements. Furthermore, the asymptotic behaviours of parton distribution functions at small and large $x$ have been studied for both the pion and the kaon. Lastly, the first three moments of parton distributions at high $Q^{2}$ scale are calculated, which are consistent with other theoretical predictions.