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

TL;DR

This paper explores the potential of muon to positron conversion as a complementary method to neutrinoless double beta decay for detecting lepton-number violation, analyzing effective operators and their implications.

Contribution

It provides a comprehensive survey of lepton-number-violating operators and discusses the relationship between different observables and new physics scales.

Findings

Muon to positron conversion can complement neutrinoless double beta decay in probing lepton-number violation.

Different effective operators influence the rates of lepton-number-violating processes.

The sensitivity of muon conversion experiments varies with the underlying new physics models.

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 $\mu^- \rightarrow e^+$ conversion, which can be explored by experiments that are specifically designed to search for $\mu^- \rightarrow e^-$ 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 $\mu^- \rightarrow e^+$ 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 $\mu^- \rightarrow e^+$ conversion offers a complementary probe of lepton-number-violating physics.