Fermion family number and the Z-Z$^{\prime}$ mixing in the 3-3-1 model with right-handed neutrinos

TL;DR

This paper demonstrates that the 3-3-1 model with right-handed neutrinos requires exactly three fermion families and derives a strict bound on the Z-Z' mixing angle based on this theoretical consistency.

Contribution

It establishes a direct link between fermion family number and Z-Z' mixing constraints within the 3-3-1 model with right-handed neutrinos.

Findings

Fermion family number must be exactly three in this model.

Derived a tight bound on Z-Z' mixing angle: -3.979×10^{-3} to 1.309×10^{-4} at 90% CL.

Showed the theoretical consistency imposes severe constraints on model parameters.

Abstract

Theoretical consistency of the 3-3-1 model with right-handed neutrinos demands that the number of family of fermions be exactly equal to three. In this brief report we show that such theoretical requirement results in a clean and severe bound on the Z-Z$^{\prime}$ mixing angle: $-3,979\times 10^{-3}<\phi<1,309\times 10^{-4} {with 90% CL}$.