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There is no guarantee that the violation of lepton number, assuming itexists, will primarily manifest itself in neutrinoless double beta decay($0\nu\beta\beta$). Lepton-number violation and lepton-flavor violation may berelated, and much-needed information regarding the physics that violates leptonnumber can be learned by exploring observables that violate lepton flavorsother than electron flavor. One of the most promising observables is $\mu^-\rightarrow e^+$ conversion, which can be explored by experiments that arespecifically designed to search for $\mu^- \rightarrow e^-$ conversion. Wesurvey lepton-number-violating dimension-five, -seven, and -nine effectiveoperators in the standard model and discuss the relationships between Majorananeutrino masses and the rates for $0\nu\beta\beta$ and $\mu^- \rightarrow e^+$conversion. While $0\nu\beta\beta$ has the greatest sensitivity to newultraviolet energy scales, its rate might be suppressed by the new physicsrelationship to lepton flavor, and $\mu^- \rightarrow e^+$ conversion offers acomplementary probe of lepton-number-violating physics.

On Lepton-Number-Violating Searches for Muon to Positron Conversion