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 $B(K^+\to\pi^+4e)=B(K^+\to\pi^+\pi^0)B(\pi^0\to4e)\approx7.0(3)\times10^{-6}$. 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, $B(K^+\to\pi^+4e,\,m_{4e}>150\,\text{MeV})=6.0(6)\times10^{-11}$.