K+→π+γγdecay in a current-current quark model and a unified approach to weak radiative kaon decays

Abstract

$K^{+}\to {\pi }^{+}\gamma \gamma$ decay as mediated by ${\mathcal{H}}_W^{\mathrm{}(\mathrm{p}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{y}-\mathrm{v}\mathrm{i}\mathrm{o}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{n}\mathrm{g})\mathrm{}}$ is studied in a modified fermion-loop model. The effect of ${\mathcal{H}}_W^{\mathrm{}(\mathrm{p}.\mathrm{v}.\mathrm{})\mathrm{}}$ is simulated by a phenomenologically constructed parity-violating meson-baryon-baryon interaction without introducing any new parameters. We find that the predicted branching ratio $r=\frac{\Gamma (K^{+}\to {\pi }^{+}\gamma \gamma )}{\Gamma (K^{+}\to \mathrm{all})}=0.64\mathrm{}\times {10}^{-6\mathrm{}}$ is of the same order of magnitude as that of the tree-graph model of Moshe and Singer.