Neutrino oscillations have proven that lepton flavor is not conserved, but we have yet to observe lepton flavor violation (LFV) in the decays of charged leptons. The Standard Model predicts that processes like the muon decay $\mu \to e \gamma$ are too rare for current or near-future experiments to detect. This, however, creates opportunities to search for new physics. Since the Standard Model expectation is essentially nil, any detected signal would be clear evidence of physics beyond our current understanding.
Recently, Professor Alexey Petrov and I investigated a rare LFV process in muonic atoms. In these systems, in the presence of appropriate new physics, a captured muon can scatter with a bound electron to produce two electrons. The rate of this process scales with the cube of the effective nuclear charge, which means that searches in heavy atoms, like lead, are more promising due to the increased overlap between muon and electron wave functions. Koike and colleagues first proposed this process in 2010.
Earlier studies focused on heavy new physics frameworks. We chose to explore the effect of light new physics particles, specifically axion-like particles (ALPs). Since light mediators avoid the suppression associated with high mass scales, we hoped the process rate would be sufficiently large. While this appeared promising in theory, light ALPs face severe constraints from flavor, astrophysics, and beam dump experiments. After including these bounds, our scan of the parameter space showed that for aluminum, the maximum surviving branching ratio remains small, at roughly $10^{-20}$. See our paper for details.
Although this process may not be the primary discovery channel for light particles like ALPs, it remains a useful complementary probe. Upcoming experiments such as Mu2e at Fermilab and COMET at J-PARC are designed for stopped muons and can search for this specific two-electron signature.
