Effects of flavor-mixings on charged kaon and pion parton distribution functions

Abstract

We investigate the charged kaon and pion parton distribution functions (PDFs) in the U(3) Nambu--Jona-Lasinio (NJL) model, considering a novel flavor-mixing interaction arising from vacuum polarization that differs from the instanton-induced 't~Hooft interaction. In this work, the proper-time regularization scheme is employed, and, effectively, it might take quark confinement into account. The gap equations, the meson masses, and the meson--quark coupling constants are calculated in the presence of flavor mixing interactions. The valence-quark distributions of the charged kaon and pion are calculated and compared with existing experimental data and JAM analysis results at scales $\mu^{2} =$ 4 and 27 GeV$^{2}$. The strength of mixing effects on the PDFs is found to be proportional to the quark effective masses and their differences. We further find that the dominant flavor mixing effects in the pion valence up-quark distribution at scales $\mu^{2} =$ 27 and 4 GeV$^2$ are around $x \simeq 0.3$ and $x \simeq 0.8$, while for the kaon, the effects are shown at around $x \simeq 0.2$ and $x \simeq 0.7$. We also find similar strength of mixing effects on the PDFs at both scales $\mu^{2} =4$ and 27 GeV$^{2}$; however, it certainly improves the pion and kaon PDFs.