Determination of coupling patterns by parallel searches for ${\mu }^{-}\to e^{+}$ and ${\mu }^{-}\to e^{-}$ in muonic atoms

Abstract

We investigate a possibility that the ${\mu }^{-}\to e^{+}$ conversion is discovered prior to the ${\mu }^{-}\to e^{-}$ 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 ${\mu }^{-}\to e^{+}$ 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 ${\mu }^{-}\to e^{+}$ rate, and the maximally allowed ${\mu }^{-}\to e^{+}$ branching ratio is $\sim 10^{-18}$ under the various bounds on RPV parameters. We show that either ${\mu }^{-}\to e^{-}$ or ${\mu }^{-}\to e^{+}$ 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.

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