Evan Rule (UCB) “Nuclear Effective Theory of μ→e Conversion”

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Abstract: Limits on the charged lepton flavor violating (CLFV) process of μe conversion are expected to improve by four orders of magnitude due to the next generation of experiments, Mu2e at Fermilab and COMET at J-PARC. The kinematics of the decay of a trapped muon are ideal for detecting a signal of CLFV, but the intervening nuclear physics presents a significant roadblock to the interpretation of experimental results. We introduce an effective theory of μe conversion formulated at the nuclear scale, which factorizes the nuclear physics from the CLFV leptonic physics, sequestering the latter quantity into unknown low-energy constants (LECs) that are probed directly by experiments. Utilizing state-of-the-art shell-model calculations of nuclear response functions, we discuss how a program of μe conversion measurements on different targets—selected for their nuclear ground-state properties—could constrain the unknown LECs. Finally, we discuss the relationship of the nuclear effective theory to higher-energy effective theories.