Muon-Electron Conversion in a Family Gauge Boson Model

TL;DR

This paper investigates muon-electron conversion in muonic atoms mediated by a family gauge boson within a $U(3)$ model, showing future experiments can probe the entire model energy scale and distinguish quark family-number assignments and mixing matrices.

Contribution

It provides a detailed analysis of muon-electron conversion rates in a family gauge boson model, highlighting the potential of upcoming experiments to explore the model's parameter space.

Findings

Next-generation experiments can cover the entire energy scale of the model.

Conversion rates are highly sensitive to quark mixing matrices.

Measurements can distinguish quark family-number assignments and individual mixing matrices.

Abstract

We study the $\mu$-$e$ conversion in muonic atoms via an exchange of family gauge boson (FGB) $A_{2}^{\ 1}$ in a $U(3)$ FGB model. Within the class of FGB model, we consider three types of family-number assignments for quarks. We evaluate the $\mu$-$e$ conversion rate for various target nuclei, and find that next generation $\mu$-$e$ conversion search experiments can cover entire energy scale of the model for all of types of the quark family-number assignments. We show that the conversion rate in the model is so sensitive to up- and down-quark mixing matrices, $U^{u}$ and $U^{d}$, where the CKM matrix is given by $V_\text{CKM} = U^{u\dagger} U^d$. Precise measurements of conversion rates for various target nuclei can identify not only the types of quark family-number assignments, but also each quark mixing matrix individually.