Title: Nuclear-Level Effective Theory of Muon-to-Electron Conversion

Abstract:  The discovery of neutrino flavor oscillations implies that there is flavor violation among the

charged leptons (CLFV).  This motivates in part two major experiments, Mu2e at Fermilab and

COMET at JPARC, that will extend current limits on CLFV rather dramatically, by four orders of

magnitude.  These involve the measurement of muon-to-electron conversion: muons will be

stopped in an Al target, where they will bind in a 1s state, then via a variety CLFV candidate mechanisms,

produce an outgoing electron with an energy of approximately the muon mass.  If the nucleus

remains in its ground state, events can be distinguished kinematically from those produced

by the free decay of the muon.  The question arises of what can and cannot be learned about

CLFV from this highly exclusive, low-energy process.  I describe a treatment in which effective theory (ET)

methods developed for an analogous process, dark matter direct detection, are adapted to produce

a nuclear-level Galilean-invariant ET for mu-to-e conversion, one respecting the available small

parameters.  This ET acts as a interface between the nuclear and particle physics of the process,

providing an efficient, complete analysis framework for experiment, yet also distilling all

relevant information needed for matching to higher level effective field theories.