Nuclear-Level Effective Theory of $\mu \to e$ Conversion

Abstract

The Mu2e and COMET $\mu \to e$ 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 $\mu \to e$ 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 $\mu \to e$ 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.

arXiv comment5 pages, 2 figures, to be submitted to PRL

References in corpus (12)

• The Effective Field Theory of Dark Matter Direct Detection
• Shell model study of the isobaric chains A=50, A=51 and A=52
• Detailed calculation of lepton flavor violating muon-electron conversion rate for various nuclei
• Signals For Supersymmetric Unification
• Model-independent WIMP Scattering Responses and Event Rates: A Mathematica Package for Experimental Analysis
• COMET Phase-I Technical Design Report
• On the model discriminating power of mu -> e conversion in nuclei
• Factorization in large-scale many-body calculations
• Nuclear-level Effective Theory of $\mu \to e$ Conversion: Formalism and Applications
• Coherent $\mu -e$ Conversion at Next-to-Leading Order
• Improved limits on lepton-flavor-violating decays of light pseudoscalars via spin-dependent $\mu \to e$ conversion in nuclei
• Next-to-leading order scalar contributions to $\mu \to e$ conversion

Cited by in corpus (7)

• Nuclear-level Effective Theory of $\mu \to e$ Conversion: Formalism and Applications
• Effective theory tower for $\mu \to e$ conversion
• Uncertainty quantification for $\mu \to e$ conversion in nuclei: charge distributions
• Ab initio calculations of overlap integrals for $\mu \to e$ conversion in nuclei
• Distinguishing charged lepton flavor violation scenarios with inelastic $\mu \to e$ conversion
• Nonrelativistic nuclear reduction for tensor couplings in dark matter direct detection and $\mu \to e$ conversion
• General Signals for Charged Lepton Flavor Violating Decays