Muon-electron conversion in a family gauge boson model

We study the μ-e conversion in muonic atoms via an exchange of family gauge boson (FGB) A21 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 μ-e conversion rate for various target nuclei, and find that next generation μ-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, Uu and Ud, where the CKM matrix is given by VCKM=Uu†Ud. 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.