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

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          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.

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          Author and article information

          Journal
          10 June 2024
          Article
          2406.06677
          41164a81-cb49-444b-abd3-b0b2b0ef0547

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

          History
          Custom metadata
          62 pages, 17 figures, python notebook with charge distributions included as supplementary material
          nucl-th hep-ex hep-ph nucl-ex

          High energy & Particle physics,Nuclear physics
          High energy & Particle physics, Nuclear physics

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