An Operator Analysis of Radiative Muon Decay

New physics beyond the Standard Model (SM) may induce new four-fermion interactions. We investigate the sensitivity of radiative muon decay, ${\mu }^{-}\to e^{-}{\bar{\nu }}_e{\nu }_{\mu }\gamma$, to such four-fermion interactions of mass dimension seven and eight. For each operator, we calculate its interference with the SM amplitude and obtain an analytic expression for the decay rate. We apply these to a log-likelihood comparison for a benchmark sample of ${10}^5$ events, and find that these operator contributions can be distinguished from the SM prediction at characteristic coefficient magnitudes between ${10}^{-9}$ and ${10}^{-8}$.