A New Determination of the (Z,A) Dependence of Coherent Muon-to-Electron Conversion

Abstract

Should muon-to-electron conversion in the field of a nucleus be found in the current generation of experiments, the measurement of the atomic number dependence of the process will become an important experimental goal. We present a new treatment of the (Z,A) dependence of coherent muon-to-electron conversion in 236 isotopes. Our approach differs from previous treatments in several ways. Firstly, we include the effect of permanent quadrupole deformation on the charged lepton flavor violating matrix elements, using the method of Barrett moments. This method also enables the addition of muonic X-ray nuclear size and shape determinations of the charge distribution to the electron scattering results used previously. Secondly, we employ a Hartree-Bogoliubov model to calculate neutron-related matrix elements for even-even nuclei. This takes into account the quadrupole deformation of the neutron distributions and the fact that neutrons are, in general, in different shell model orbits than protons. The calculated conversion rates differ from previous calculations, particularly in the region of large permanent quadrupole deformation. Finally, we propose an alternative normalization of the muon-to-electron conversion rated, which related more closely to what a given experiment acturally measures, and better separate lepton physics from nuclear physics effects.

23 pages, 12 figures

References in corpus (12)

• Technical design of the phase I Mu3e experiment
• Nuclear mass table in deformed relativistic Hartree-Bogoliubov theory in continuum, II: Even-$Z$ nuclei
• Muon decay in orbit: spectrum of high-energy electrons
• The exact Schur index in closed form
• Nuclear-level Effective Theory of $\mu \to e$ Conversion: Formalism and Applications
• Reach and complementarity of $\mu \to e$ searches
• 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
• First Determination of the 27Al Neutron Distribution Radius from a Parity-Violating Electron Scattering Measurement
• Analysis of Lepton Flavor Violating τ^\pm \to μ^\pm μ^\pm μ^\mp Decays
• Isotope dependence of muon decay in orbit
• Distinguishing charged lepton flavor violation scenarios with inelastic $\mu \to e$ conversion

Cited by in corpus (1)

• Ab initio calculations of overlap integrals for $\mu \to e$ conversion in nuclei