Departures from the Eightfold Way. III. Pseudoscalar-Meson Electromagnetic Masses

Abstract

The leading contributions to the ${\pi }^{+}-{\pi }^0$ and $K^{+}-K^0$ mass differences are calculated. The contributions of pseudoscalar-meson and vector-meson intermediate states are considered, and the Feynman integrations are performed assuming very general momentum dependence at the vertices. Using form factors having poles at the vector-meson masses, and the unitary-symmetric vector mixing model of Coleman and Schnitzer, we find $m_{\pi +}-m_{\pi 0}=4.9\mathrm{}$ MeV and ${m_K}^{+}-{m_K}^0=2.9\mathrm{}$ MeV. It is difficult to give a reliable estimate of the errors in these calculations; we believe they are correct to within 1 MeV. The uncertainty lies partly in the determination of the $\gamma -\rho -\pi$ coupling constant and partly in the dynamical assumptions. When the scalar-meson contribution suggested by Coleman and Glashow is included, the $\pi$-meson mass difference is unchanged and the $K$-meson mass difference becomes ${m_K}^{+}-{m_K}^0=-1.4\mathrm{}$ MeV. Our numerical values have been tabulated without discussion in two earlier papers of this series.