Nuclear muon-positron conversion mediated by Majorana neutrinos

We study lepton number violating (LNV) process of muon-positron conversion in nuclei mediated by the exchange of light and heavy Majorana neutrinos. Nuclear structure calculations have been carried out for the case of experimentally interesting nucleus 48Ti in the framework of renormalized proton-neutron Quasiparticle Random Phase Approximation. We demonstrate that the imaginary part of the amplitude of light Majorana neutrino exchange mechanism gives an appreciable contribution to the muon-positron conversion rate. This specific feature is absent in the allied case of neutrinoless double beta decay. Using the present neutrino oscillations, tritium beta decay, accelerator and cosmological data we derived the limits on the effective masses of light <m>_{\mu e} and heavy <M_N^{-1}>_{\mu e} neutrinos. The expected rates of muon-positron nuclear conversion, corresponding to these limits, were found to be so small that even within a distant future the muon-positron conversion experiments will hardly be able to detect the neutrino signal. Therefore, searches for this LNV process can only rely on the presence of certain physics beyond the trivial extension of the Standard Model by inclusion of massive Majorana neutrinos.