The 27-plet contributions to the CP-conserving $K\rightarrow \pi l^+l^-$ decays

Abstract

We revisit the the rare kaon decays $K\to \pi l^+l^-$ which are of interest specially due to the recent measurements of the charged kaon decay spectra. We compute the contribution of the 27-plet to the decay amplitudes in one loop SU(3) Chiral Perturbation Theory. We estimate the resulting impact to be $\sim 10%$ to the branching ratios of the charged kaon decays, and also noticeably influence the shape of the spectra. With current values of the constants $G_8$ associated with the octet and $G_{27}$ associated with the 27-plet, the contribution of the latter pushes the spectrum in the correct direction for the charged lepton spectra. We also discuss the impact for the neutral decay rates and spectra.