Standard Model estimate of $K^{+}\to {\pi }^{+}4e$ branching ratio

Abstract

The branching ratio of the $K^{+}\to {\pi }^{+}{e}^{+}{e}^{-}{e}^{+}{e}^{-}$ ($K^{+}\to {\pi }^{+}4e$) decay is calculated at leading order in the Standard Model. The dominance of the neutral-pion pole determines the overall branching ratio to be $B(K^{+}\to {\pi }^{+}4e)=B(K^{+}\to {\pi }^{+}{\pi }^0)B({\pi }^0\to 4e)\approx 7.0(3)\times 10^{-6}$. The significance of this contribution is very much concentrated in the context of the whole available phase space, throughout most of which the one-photon-exchange topology is prevalent in turn. It is thus interesting to present branching ratios for only parts of the allowed kinematical region. We find, for instance, $B(K^{+}\to {\pi }^{+}4e,m_{4e}>150\text{MeV})=6.0(6)\times 10^{-11}$.

Comments: 7 pages, 4 figures, 1 table; v2: version accepted for publication in PRD, minor text improvements