Determination of coupling patterns by parallel searches for μ− → e+ and μ− → e− in muonic atoms

Abstract

We investigate a possibility that the μ−→e+ conversion is discovered prior to the μ−→e− conversion, and its implications to the new physics search. We focus on the specific model including the mixing of the SU(2)L doublet- and singlet-type scalar leptoquarks, which induces not only the lepton flavor violation but also the lepton number violation. Such a structure is motivated by R-parity violating (RPV) supersymmetric models, where a sbottom mediates the conversion processes. We formulate the μ−→e+ rate in analogy with the muon capture in a muonic atom, and numerically evaluate it using several target nuclei. The lepton flavor universality test of pion decay directly limits the μ−→e+ rate, and the maximally allowed μ−→e+ branching ratio is ∼10−18 under the various bounds on RPV parameters. We show that either μ−→e− or μ−→e+ signals can be discovered in near future experiments. This indicates that parallel searches for these conversions will give us significant information on the pattern of coupling constants.