Electromagnetic self-energies of pseudoscalar mesons and Dashen's theorem

Abstract

The calculation of the electromagnetic mass shifts of $\pi$, $K$ mesons is studied using a model incorporating chiral symmetry and vector dominance. Significant SU(3) breaking to Dashen's theorem is found, allowing a resolution of the long-standing discrepancy between the quark-mass ratio $\frac{(m_d-m_u)}{m_s}$ found from $\eta \to 3\pi$ decay and that from the $K^{+}-K^0$ mass difference.