Coherent $\mu -e$ Conversion at Next-to-Leading Order

Abstract

We analyze next-to-leading order (NLO) corrections and uncertainties for coherent $\mu -e$ conversion . The analysis is general but numerical results focus on ${}^{27}\text{Al}$, which will be used in the Mu2E experiment. We obtain a simple expression for the branching ratio in terms of Wilson coefficients associated with possible physics beyond the Standard Model and a set of model-independent parameters determined solely by Standard Model dynamics. For scalar-mediated conversion, we find that NLO two-nucleon contributions can significantly decrease the branching ratio, potentially reducing the rate by as much as 50%. The pion-nucleon $\sigma$-term and quark masses give the dominant sources of parametric uncertainty in this case. For vector-mediated conversion, the impact of NLO contributions is considerably less severe, while the present theoretical uncertainties are comparable to parametric uncertainties.

36 pages, 2 figures, 7 tables

References in corpus (9)

• Nucleon Electromagnetic Form Factors
• High Precision determination of the pi, K, D and D_s decay constants from lattice QCD
• Lattice QCD at the physical point: light quark masses
• Extracting the sigma-term from low-energy pion-nucleon scattering
• Improved predictions for $\mu \to e$ conversion in nuclei and Higgs-induced lepton flavor violation
• Muon decay in orbit: spectrum of high-energy electrons
• Determination of the Axial-Vector Weak Coupling Constant with Ultracold Neutrons
• First-principle calculations of Dark Matter scattering off light nuclei
• Mu2e Conceptual Design Report

Cited by in corpus (12)

• The Role of Lattice QCD in Searches for Violations of Fundamental Symmetries and Signals for New Physics
• Nuclear-level Effective Theory of $\mu \to e$ Conversion: Formalism and Applications
• Revisiting Generalized Two Higgs Doublet Model in the Light of Muon Anomaly and Lepton Flavor Violating Decays at HL-LHC
• Effective theory tower for $\mu \to e$ conversion
• Next-to-leading order scalar contributions to $\mu \to e$ conversion
• Isotope dependence of muon-to-electron conversion
• Nuclear-Level Effective Theory of $\mu \to e$ Conversion
• Generalized 2HDM with wrong-sign lepton Yukawa coupling, in light of $g_{\mu }-2$ and lepton flavor violation at the future LHC
• Isotope dependence of muon decay in orbit
• Scalar triplet leptogenesis in the presence of right-handed neutrinos with S3 symmetry
• Distinguishing charged lepton flavor violation scenarios with inelastic $\mu \to e$ conversion
• A New Determination of the (Z,A) Dependence of Coherent Muon-to-Electron Conversion