The Mu2e and COMET μ→e conversion experiments are expected to
significantly advance limits on new sources of charged lepton flavor violation
(CLFV). Almost all theoretical work in the field has focused on just two
operators. However, general symmetry arguments lead to a μ→e
conversion rate with six response functions, each of which, in principle, is
observable by varying nuclear properties of targets. We construct a
nucleon-level nonrelativistic effective theory (NRET) to clarify the
microscopic origin of these response functions and to relate rate measurements
in different targets. This exercise identifies three operators and their small
parameters that control the NRET operator expansion. We note inconsistencies in
past treatments of these parameters. The NRET is technically challenging,
involving 16 operators, several distorted electron partial waves, bound muon
upper and lower components, and an exclusive nuclear matrix element. We
introduce a trick for treating the electron Coulomb effects accurately, which
enables us to include all of these effects while producing transition densities
whose one-body matrix elements can be evaluated analytically, greatly
simplifying the nuclear physics. We derive bounds on operator coefficients from
existing and anticipated μ→e conversion experiments. We discuss
how similar NRET formulations have impacted dark matter phenomenology, noting
that the tools this community has developed could be adapted for CLFV studies.Comment: 5 pages, 2 figures, to be submitted to PR