Improved predictions for $\mu\to e$ conversion in nuclei and Higgs-induced lepton flavor violation

TL;DR

This paper analyzes Higgs-induced lepton flavor violation in muon to electron conversion in nuclei, highlighting reduced theoretical uncertainties using $SU(2)$ Chiral Perturbation Theory and lattice QCD, and compares experimental bounds across models.

Contribution

It introduces a novel approach using $SU(2)$ Chiral Perturbation Theory and lattice QCD to accurately assess hadronic uncertainties in Higgs-mediated $ o e$ conversion, improving upon traditional methods.

Findings

Higgs-induced $ o e$ conversion is highly sensitive to new physics.

The $SU(2)$ Chiral Perturbation Theory approach reduces hadronic uncertainties.

Current and future experiments place stringent bounds on Higgs-mediated lepton flavor violation.

Abstract

Compared to $\mu \to e \gamma$ and $\mu \to e e e$, the process $\mu \to e$ conversion in nuclei receives enhanced contributions from Higgs-induced lepton flavor violation. Upcoming $\mu \to e$ conversion experiments with drastically increased sensitivity will be able to put extremely stringent bounds on Higgs-mediated $\mu \to e$ transitions. We point out that the theoretical uncertainties associated with these Higgs effects, encoded in the couplings of quark scalar operators to the nucleon, can be accurately assessed using our recently developed approach based on $SU(2)$ Chiral Perturbation Theory that cleanly separates two- and three-flavor observables. We emphasize that with input from lattice QCD for the coupling to strangeness $f_s^N$, hadronic uncertainties are appreciably reduced compared to the traditional approach where $f_s^N$ is determined from the pion--nucleon $\sigma$-term by means of an $SU(3)$ relation. We illustrate this point by considering Higgs-mediated lepton flavor violation in the Standard Model supplemented with higher-dimensional operators, the two-Higgs-doublet model with generic Yukawa couplings, and the Minimal Supersymmetric Standard Model. Furthermore, we compare bounds from present and future $\mu \to e$ conversion and $\mu \to e \gamma$ experiments.