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

Abstract

There is no guarantee that the violation of 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 lepton number can be learned by exploring observables that violate lepton flavors other than electron flavor. One of the most promising observables is ${\mu }^{-}\to e^{+}$ conversion, which can be explored by experiments that are specifically designed to search for ${\mu }^{-}\to e^{-}$ 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 ${\mu }^{-}\to e^{+}$ 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 ${\mu }^{-}\to e^{+}$ conversion offers a complementary probe of lepton-number-violating physics.

Comments: 13 pages, 7 figures; updated to include modified results for two operators and additional references