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

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.

Comments: 13 pages, 9 figures