We present a class of constraints on products and combinations of Yukawa couplings for $R$ parity violating (${\mathrm{R̸}}_p$) and lepton flavor conserving as well as violating semileptonic decays of $K$ mesons into light pseudoscalar mesons along with two charged leptons at $1\sigma$ and $2\sigma$ levels. We compare the constraints obtained by semileptonic rare decays with pure leptonic rare decays and find that most of these bounds are now improved over the existing ones. We also study the forward-backward asymmetry in the decays of $K^{+}\to {\pi }^{+}{l}^{+}{l}^{-}$ ($l=e$ and $\mu$) in the absence of tensor terms. The asymmetry is found to be up to $O({10}^{-3})$ ($O({10}^{-1})$) for the electron and muon modes, respectively. The asymmetry is found to be as large as $O({10}^{-1})$ in the case of $K^{+}\to {\pi }^{+}{\mu }^{+}{\mu }^{-}$.

• Received 9 May 2007

DOI:https://doi.org/10.1103/PhysRevD.76.114005