Nucleon-level Effective Theory of μ→e Conversion

The Mu2E and COMET μ→ e collaborations may soon advance branching ratio sensitivities by four orders of magnitude, further constraining new sources of charged lepton flavor violation (CLFV). Here we formulate a non-relativistic nucleon-level effective theory (ET) for this process, in order to clarify what can and cannot be learned about CLFV operator coefficients from elastic μ → e conversion. Utilizing state-of-the-art shell model wave functions, we derive bounds on operator coefficients from existing μ → e conversion and μ → eγ results, and estimate the improvement in these bounds that will be possible if Mu2E, COMET, and MEG II reach their design goals. In the conversion process, we employ a treatment of the lepton Coulomb physics that is very accurate, yields transparent results, and preserves connections to standard-model processes like β decay and μ capture. The formulation provides a bridge between the nuclear physics needed in form factor evaluations and the particle physics that relates low-energy constraints from μ → e conversion to UV sources of CLFV.