Impact of Charge Symmetry Breaking on Gluon and Sea Quark Distributions in the Pion and Kaon

TL;DR

This study investigates how charge symmetry breaking from u and d quark mass differences affects gluon and sea quark distributions in pions and kaons using the NJL model, revealing small but notable effects consistent with lattice QCD and global fits.

Contribution

First analysis of charge symmetry breaking effects on gluon and sea quark distributions in pions and kaons within the NJL model framework.

Findings

CSB effects on pion gluon distribution are about 1.3% at x≈1.

CSB effects on pion sea quarks are about 2.0% at x≈1.

CSB effects on kaon distributions are smaller, around 0.3-0.5%. at x≈1.

Abstract

In this exploratory study, I present, for the first time, the implications of the charge symmetry breaking (CSB) that arise from the $u$ and $d$ quark mass differences on gluon and sea quark distribution functions of the pion and kaon in the framework of the Nambu--Jona-Lasino (NJL) model, which is a quark-level chiral effective theory of QCD, with the help of the proper-time regularization scheme to simulate color confinement of QCD. From the analysis, one finds that the charge symmetry (CS) gluon distribution for the pion has a good agreement with the prediction results obtained from the recent lattice QCD simulation and JAM global fit QCD analysis at a higher scale of $Q^2 =$ 5 GeV$^2$. The size of the CSB effects on gluon and sea quark distributions for the pion with the realistic ratios of $m_u/m_d = 0.5$ at $Q^2 =$ 5 GeV$^2$ are respectively estimated by 1.3\% and 2.0\% at $x \simeq 1$ in comparison with those for $m_u/m_d = 1.0$, while those for the kaon are approximately about 0.3\% and 0.5\% at $ x \simeq 1$, respectively. A remarkable result is found that the CSB effects on gluon distribution for the kaon are smaller than that for the pion, which has a similar prediction result as that for the CS case.