Next-to-leading order scalar contributions to $\mu\rightarrow e$ conversion

TL;DR

This paper calculates muon-to-electron conversion rates in nuclei within scalar-mediated lepton flavor violation models, including NLO corrections in chiral effective theory, revealing a significant impact on theoretical predictions and experimental tests.

Contribution

It provides the first comprehensive NLO analysis of scalar contributions to $$ conversion, correcting previous inaccuracies and quantifying uncertainties.

Findings

NLO contributions modify amplitudes by about 10%

Uncertainty dominated by nucleon sigma terms

Results inform future experimental searches for CLFV

Abstract

Within a class of models in which lepton flavor violation is induced dominantly by scalar particle exchanges, we estimate the $\mu \to e$ conversion rate in several nuclei. We include next-to-leading order (NLO) terms in the one- and two-nucleon interactions in chiral effective theory, rectifying some incorrect results in the previous literature. We provide an uncertainty budget for the conversion rates and we find that NLO contributions affect the amplitudes at the level of $10\%$, which could be larger than the uncertainty on the leading order couplings, dominated by the strange and non-strange nucleon sigma terms. We study the implications of our results for testing Higgs-mediated CLFV in the future by combining results from various experimental searches, such as $\mu \to e$ conversion in multiple target nuclei and $\mu \to e \gamma$.