Minimal Supersymmetric Standard Model

The quantity RK = Γ(K → eν)/Γ(K → μν) studied by the experiment NA62 at CERN is known to probe lepton-flavour violating (LFV) parameters of the Minimal Supersymmetric Standard Model (MSSM). A non-zero parameter δ RR can open the decay channel K → eντ and enhance RK over its Standard-Model value. In the region of the parameter space probed by NA62 the contribution from a bino-stau loop diagram is numerically dominant and the mixing between left-handed and right-handed staus is important. For large values of the stau mixing angle θτ the commonly adopted mass insertion approximation is not accurate. We therefore express the supersymmetric contribution to RK in terms of the mass of the lightest stau eigenstate, the mixing angle θτ , and other relevant MSSM parameter such as tanβ and the charged-Higgs boson mass MH and plot the parameter regions constrained by RK . We further study to which extent RK can be depleted through MSSM contributions interfering destructively with the SM amplitude for K → eνe. This lepton-flavour conserving (LFC) mechanism involves the parameter combination |δ13 LLδ13 RR|, which can be constrained with a naturalness consideration for the electron mass or with the measurement of the anomalous magnetic moment of the electron. The LFC effect on RK is marginal, an NA62 measurement of RK significantly below the Standard Model expectation would indicate physics beyond the MSSM.