# Effects of charge symmetry breaking on form factors of the pion and kaon

## TL;DR

This paper investigates how charge symmetry breaking due to quark mass differences affects the electromagnetic form factors and parton distribution functions of the pion and kaon using a confining NJL model.

## Contribution

It provides a detailed analysis of charge symmetry breaking effects on meson form factors and PDFs within a dressed quark framework based on the Bethe-Salpeter equation.

## Key findings

- Significant charge symmetry breaking effects in meson electromagnetic form factors.
- Smaller charge symmetry breaking effects observed in parton distribution functions.
- Charge symmetry breaking effects are prominent for realistic quark mass ratios.

## Abstract

Effects of charge symmetry breaking associated with the $u$ and $d$ quark mass difference in the elastic form factors of the pion and kaon are presented. We use a confining version of the Nambu--Jona-Lasinio model. The pion and kaon are described as a dressed quark and antiquark bound states governed by the Bethe-Salpeter equation, and exhibit the properties of Goldstone bosons, with the pion mass difference given by $m_{\pi^{+}}^2 - m_{\pi^{0}}^2 \propto (m_u -m_d)^2$ as demanded by dynamical chiral symmetry breaking. We found significant charge symmetry breaking effects for realistic current quark mass ratios ($m_u/m_d \sim 0.5$) in the quark electromagnetic form factors of the pion and kaon. We also report the effects of charge symmetry breaking on the parton distribution functions, which are rather smaller than those found in the electromagnetic form factors.