The muon-positron conversion in nuclei mediated by light Majorana neutrinos

We study the lepton number violating muon-positron conversion in nuclei mediated by the exchange of virtual light Majorana neutrinos. We found that a previously overlooked imaginary part of this amplitude plays an important role. The numerical calculation has been made for the experimentally interesting muon-positron conversion in Ti48 using realistic renormalized proton-neutron QRPA wave functions. We also discuss the very similar case of the neutrinoless double beta decay of Ca48 The ratio of muon-positron conversion over the total muon absorption has been computed taking into account the current constraints from neutrino oscillation phenomenology. We compare our results with the experimental limits as well as with previous theoretical predictions. We have found that the Majorana neutrino mode of muon-positron conversion in Ti48 is too small to be measurable in the foreseeable future.