Rare decays of Muons and Kaons as a probe of new fundamental symmetries of nature

Abstract

The predictions for rare decays of Muons and Kaons in Left-right symmetric and general supersymmetric theories of weak interactions are discussed. It is pointed out that rare muon processes such as muonium to antimuonium conversion, μ − →ρ −ν ρ ν μ provide sensitive tests of left-right symmetric theories if the scale of right-handed interactions is in the TeV range. They are not only predicted to be in the observable range for the proposed experiments at PSI and Los Alamos but if the neutrino spectrum of the model is of the eV:KeV:MeV type,then cosmological constraints imply a lower bound on the rates for these processes which when violated will rule out this class of models. Other rare muon decays such as μ → ργ and μ → 3 ρ are also predicted to be in the observable range in the next generation of experiments. In the kaon sector, the muon polarization in the decays K L → μ + μ − is also predicted to be large if CP-violation is included in these models via the phases of coupling constants and vacuum expectation values. We next discuss the implications of the general class of supersymmetric standard models which include R-parity violating interactions. We find that several rare muon processes as well as Kaon decays can occur at observable rate in these models providing a separate motivation for carrying out the next round of high sensitive muon and kaon decay experiments. We then briefly comment on making the left-right model supersymmetric and its implications for the same processes.