$\mu^- \to e^-\gamma$ in a muonic atom as a probe for effective lepton flavor violating operators involving photon fields

TL;DR

This paper explores using muonic atoms to detect charged lepton flavor violation via the $0^- o e^- 0$ process, highlighting its sensitivity to photon-related operators and potential for future experiments.

Contribution

It introduces a novel method to probe CLFV operators involving photons through muonic atom decays, expanding beyond traditional free muon decay searches.

Findings

Decay rate formula derived for the process.

Non-monochromatic spectra of emitted particles analyzed.

Potential experimental sensitivity shown to be promising.

Abstract

We propose the $\mu^-\to e^-\gamma$ process in a muonic atom as a novel means to investigate charged lepton flavor violation (CLFV). We demonstrate its sensitivity in probing effective CLFV operators associated with both single and double photon fields. In comparison to $\mu^+\to e^+\gamma$ using free positive muon decays at rest, the emitted electron and photon in $\mu^-\to e^-\gamma$ exhibit non-monochromatic spectra, presenting non-trivial case. We derive the decay rate formula and demonstrate that the potential rate of the process is significant enough to motivate exploration in future muon CLFV experiments.