Future experimental improvement for the search of lepton-number-violating processes in the eμ sector

The conservation of lepton flavor and total lepton number are no longer guaranteed in the Standard Model after the discovery of neutrino oscillations. The μ-+N(A,Z)→e++N(A,Z-2) conversion in a muonic atom is one of the most promising channels to investigate the lepton number violation processes, and measurement of the μ - e+ conversion is planned in future μ - e- conversion experiments with a muonic atom in a muon-stopping target. This article discusses experimental strategies to maximize the sensitivity of the μ - e+ conversion experiment by introducing the new requirement of the mass relation of M(A,Z-2)<M(A,Z-1), where M(A,Z) is the mass of the muon-stopping target nucleus, to eliminate the backgrounds from radiative muon capture. The sensitivity of the μ - e+ conversion is expected to be improved by 4 orders of magnitude in forthcoming experiments using a proper target nucleus that satisfies the mass relation. The most promising isotopes found are Ca40 and S32.