Uncertainty quantification for $\mu \to e$ conversion in nuclei: charge distributions

Abstract

Predicting the rate for $\mu \to e$ conversion in nuclei for a given set of effective operators mediating the violation of lepton flavor symmetry crucially depends on hadronic and nuclear matrix elements. In particular, the uncertainties inherent in this non-perturbative input limit the discriminating power that can be achieved among operators by studying different target isotopes. In order to quantify the associated uncertainties, as a first step, we go back to nuclear charge densities and propagate the uncertainties from electron scattering data for a range of isotopes relevant for $\mu \to e$ conversion in nuclei, including ${}^{40,48}$Ca, ${}^{48,50}$Ti, and ${}^{27}$Al. We provide as central results Fourier-Bessel expansions of the corresponding charge distributions with complete covariance matrices, accounting for Coulomb-distortion effects in a self-consistent manner throughout the calculation. As an application, we evaluate the overlap integrals for $\mu \to e$ conversion mediated by dipole operators. In combination with modern ab-initio methods, our results will allow for the evaluation of general $\mu \to e$ conversion rates with quantified uncertainties.

63 pages, 17 figures, python notebook with charge distributions included as supplementary material; journal version

References in corpus (11)

• A nucleus-dependent valence-space approach to nuclear structure
• Two-pion exchange electromagnetic current in chiral effective field theory using the method of unitary transformation
• Kaon electromagnetic form factors in dispersion theory
• Improved predictions for $\mu \to e$ conversion in nuclei and Higgs-induced lepton flavor violation
• Muon decay in orbit: spectrum of high-energy electrons
• Isospin-breaking effects in the two-pion contribution to hadronic vacuum polarization
• Nuclear electromagnetic currents to fourth order in chiral effective field theory
• Lepton flavor violating quarkonium decays
• Statistical uncertainties of a chiral interaction at next-to-next-to leading order
• Isospin-breaking effects in the three-pion contribution to hadronic vacuum polarization
• Next-to-leading order scalar contributions to $\mu \to e$ conversion

Cited by in corpus (6)

• Improved structure of calcium isotopes from ab initio calculations
• Ab initio computations of the fourth-order charge density moments of ${}^{48}$Ca and ${}^{208}$Pb
• Ab initio calculations of overlap integrals for $\mu \to e$ conversion in nuclei
• Neutron-rich nuclei and neutron skins from chiral low-resolution interactions
• From Higgs physics to lepton flavour violation: current bounds and future prospects for vector-like lepton models
• Parameterizations of Electron Scattering Form Factors for Elastic Scattering and Electro-Excitation of Nuclear States for ${}^{27}\mathrm{Al}$ and ${}^{40}\mathrm{Ca}$