Some rare decay modes of theKmeson in a current-current quark model. I.K→πl+l−decay

Abstract

$K^{+}\to {\pi }^{+}{l}^{+}{l}^{-}$ decay is calculated in a zero-parameter modified baryon-loop model which has proven successful in describing the weak radiative kaon decays. The weak Hamiltonian is phenomenologically constructed from one-baryon octet matrix elements. The predicted branching ratio of the loop model $r_{+}\left(e^{+}{e}^{-}\right)=\frac{\Gamma (K^{+}\to {\pi }^{+}{e}^{+}{e}^{-})}{\Gamma (K^{+}\to \mathrm{all})}=1.6\mathrm{}\times {10}^{-6\mathrm{}}$ [with $r_{+}\left({\mu }^{+}{\mu }^{-}\right)=0.3\mathrm{}\times {10}^{-6\mathrm{}}$] compares reasonably with the prediction of a recent gauge-theory calculation of Lee and Gaillard, $r_{+}^{\mathrm{G}.\mathrm{T}.\mathrm{}}\left(e^{+}{e}^{-}\right)\sim {10}^{-6\mathrm{}}$ (with acceptable values ranging between 3 × ${10}^{-6\mathrm{}}$ and 0.5 × ${10}^{-6\mathrm{}}$) and is to be compared with the presently available experimental upper bound $r_{+}^{\exp }\left(e^{+}{e}^{-}\right)<\mathrm{}0.4\mathrm{}\times {10}^{-6\mathrm{}}$. We also find the ratio $\frac{\Gamma (K_S^0\to {\pi }^0{e}^{+}{e}^{-})}{\Gamma (K^{+}\to {\pi }^{+}{e}^{+}{e}^{-})}$ to be essentially zero in the loop model, as opposed to its value of unity in the gauge-model calculation.