Muon to positron conversion

TL;DR

This paper reviews the theoretical motivation, experimental status, and future prospects of muon to positron conversion, a lepton number violating process that could reveal physics beyond the Standard Model.

Contribution

It provides a comprehensive review of muon to positron conversion, emphasizing background challenges and the potential for discovering new physics beyond the Standard Model.

Findings

Radiative muon capture is a potentially dominant background.

Current experiments set upper limits on muon to positron conversion.

Future experiments aim to improve sensitivity to this rare process.

Abstract

Lepton flavor violation (LFV) has been discovered in the neutrino sector by neutrino oscillation experiments. The minimally extended Standard Model (SM) to include neutrino masses allows LFV in the charged sector (CLFV) at the loop-level, but at rates that are too small to be experimentally observed. Lepton number violation (LNV) is explicitly forbidden even in the minimally extended SM, where the observation of a LNV process would be unambiguous evidence of physics beyond the SM. The search for the LNV and CLFV process $\mu^- + N(A,Z) \to e^+ + N'(A,Z-2)$ (referred to as $\mu^- \to e^+$ conversion) is a complementary LNV channel to neutrinoless double beta decay searches, sensitive to potential flavor effects in the neutrino mass generation mechanism. A theoretical motivation for $\mu^- \to e^+$ conversion is presented along with a review of the status of past $\mu^- \to e^+$ conversion experiments and future prospects. Special attention is taken to understanding an uncertain and potentially dominant background for these searches, radiative muon capture, and its potential impacts on current and future $\mu^- \to e^+$ searches.