Rare Decays of $K$ and $B$ Mesons Revisited
The rare decays of mesons are higher order effects in weak interactions. The main contributions to such decay processes are from the Z-penguin, the photonpenguin and the box diagram. At the quark level, these contributions are well known. However, when considering the corresponding physical hadronic processes, a knowledge of how hadronic states are expressed in terms of quarks. In this paper, we suggest a simplistic way to relate the quark level process to the hadronic process. For simplicity, we consider here only the decays of pseudoscalar mesons. The meson-quark coupling is described in terms of a gamma-5 coupling with a constant coupling constant. We apply the model to processes in which meson M1 decays to meson M2 with the emissions of neutrino pair and charged lepton pair. In calculating the decay rates, a cut-off momentum lamda is introduced to control the divergent triangle integral over the internal momentum. The results of our calculation is compared to experimental data on the decay rates for K- and B-meson decays.