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.