Constraints on charged lepton flavor violation from muon-to-electron conversion in nuclei

Muon-to-electron conversion is one of our most sensitive probes of charged lepton flavor violation (CLFV). Depending on the underlying BSM mechanism, the next-generation experiments Mu2e at Fermilab and COMET at J-PARC may probe new physics at scales up to 10,000 TeV. Complementary physics information can be obtained by varying the nuclear target. If the process is mediated by exchange of a heavy scalar particle, it is possible to predict the expected CLFV branching ratio with a well-understood uncertainty, yielding rigorous constraints on the parameters of candidate UV models. Beyond this simplest coherent scenario, the most general CLFV interaction including spin- and velocity-dependent nuclear responses was recently constructed. We discuss this progress and the outstanding challenges towards leveraging the full power of Mu2e and COMET to probe BSM physics.