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

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 $m_{π^{+}}^2 - m_{π^{0}}^2 \propto (m_u -m_d)^2$ 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.