Abelian charge inspired by family number

TL;DR

This paper proposes a novel $U(1)$ gauge symmetry inspired by family number, linking it to anomaly cancellation conditions and exploring implications for neutrino masses, the $W$-boson mass anomaly, FCNC, and collider physics.

Contribution

It introduces a new $U(1)$ gauge symmetry based on family number, connecting anomaly cancellation to family and color numbers, with implications for particle physics phenomena.

Findings

A new $U(1)$ symmetry related to family number is consistent with anomaly cancellation.

Potential explanations for neutrino mass and $W$-boson mass anomaly are discussed.

Implications for FCNC processes and collider experiments are analyzed.

Abstract

Quark has an electric charge either $-1/3$ or $2/3$ and a baryon number $1/3$, where the divisions $3$'s match the color number. Although the electric charge and the baryon number have a nature distinct from the color charge, the matching is necessary for the standard model or a relevant $B-L$ extension consistent at quantum level, since the relevant anomaly $[SU(2)_L]^2U(1)_A$ for $A=Y$ or $B-L$ must vanish. If elementary particles have a new $U(1)$ charge differently from $A$, such anomaly is not cancelled for each family. However, if we demand that the anomaly is cancelled over all families, this relates the color number to the family number instead of the electric charge and baryon number, and interestingly the family number guides us to a novel $U(1)$ theory. We will discuss the implication of this theory for neutrino mass, recent $W$-boson mass anomaly, FCNC, and particle colliders.