Future experimental improvement for the search of lepton-number-violating processes in the 𝑒⁢𝜇 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 ⁴⁰Ca and ³²S.