# Valence-quark distributions of pions and kaons in a nuclear medium

## TL;DR

This study investigates how valence-quark distributions in pions and kaons are affected by nuclear medium using combined NJL and quark-meson coupling models, revealing density-dependent modifications consistent with experimental data.

## Contribution

It introduces a novel combined modeling approach to analyze in-medium valence-quark distributions in mesons, highlighting density effects on quark properties and distributions.

## Key findings

- Valence quark distributions in vacuum match experimental data.
- In-medium u-quark distribution in pion remains nearly unchanged.
- Ratios of valence quark distributions in kaons increase with density, showing different x-dependence.

## Abstract

In-medium valence-quark distributions of $\pi^+$ and $K^+$ mesons in symmetric nuclear matter are studied by combining the Nambu--Jona-Lasinio model and the quark-meson coupling model. The in-medium properties of the current quarks, which are used as inputs for studying the in-medium pion and kaon properties in the Nambu--Jona-Lasinio model, are calculated within the quark-meson coupling model. The light-quark condensates, light-quark dynamical masses, pion and kaon decay constants, and pion- and kaon-quark coupling constants are found to decrease as nuclear density increases. The obtained valence quark distributions in vacuum for both the $\pi^+$ and $K^+$ could reasonably describe the available experimental data over a wide range of Bjorken-$x$. The in-medium valence $u$-quark distribution in the $\pi^+$ at $Q^2=16~\mbox{GeV}^2$ is found to be almost unchanged compared to the in-vacuum case. However, the in-medium to in-vacuum ratios of both the valence $u$-quark and valence $s$-quark distributions of the $K^+$ meson at $Q^2=16~\mbox{GeV}^2$ increase with nuclear matter density, but show different $x$-dependence. Namely, the ratio for the valence $u$-quark distribution increases with $x$, while that for the valence $s$ quark decreases with $x$. These features are enhanced at higher density regions.