Lepton-number-violating searches for muon to positron conversion

There is no guarantee that the violation of the lepton number, assuming it exists, will primarily manifest itself in neutrinoless double beta decay (0 nu beta beta). Lepton-number violation and lepton-flavor violation may be related, and much-needed information regarding the physics that violates the lepton number can be learned by exploring observables that violate lepton flavors other than the electron flavor. One of the most promising observables is the mu(-) -> e(+) conversion, which can be explored by experiments that are specifically designed to search for the mu(-) -> e(-) conversion. We survey lepton-number violating dimension-five, -seven, and -nine effective operators in the standard model and discuss the relationships between Majorana neutrino masses and the rates for 0 nu beta beta and the mu(-) -> e(+) conversion. While 0 nu beta beta has the greatest sensitivity to new ultraviolet energy scales, its rate might be suppressed by the new physics relationship to lepton flavor, and the mu(-) -> e(+) conversion offers a complementary probe of lepton-number-violating physics.