Explaining Fermions Mass and Mixing Hierarchies through $U(1{)}_X$ and $Z_2$ Symmetries

Abstract

For understanding the hierarchies of fermion masses and mixing, we extend the Standard Model gauge group with \( U(1)_X \) and \( Z_2 \) symmetry. The field content of the Standard Model is augmented by three heavy right-handed neutrinos, two new scalar singlets, and a scalar doublet. \( U(1)_X \) charges of different fields are determined after satisfying anomaly cancellation conditions. In this scenario, the fermion masses are generated through higher-dimensional effective operators with \( O(1) \) Yukawa couplings. The small neutrino masses are obtained through type-1 seesaw mechanism using the heavy right-handed neutrino fields, whose masses are generated by the new scalar fields. We discuss the flavour-changing neutral current processes that arise due to the sequential nature of \( U(1)_X \) symmetry. We have written effective higher-dimensional operators in terms of renormalizable dimension-four operators by introducing vector-like fermions.

Comments: matches published version