Abelian charge inspired by family number

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 $[SU(2{)}_L{]}^{2}U(1{)}_A$ 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.

arXiv comment21 pages, 3 figures; Yukawa couplings corrected and presentation improved; Matches journal version

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• Phenomenology of a minimal extension of the standard model with a family-dependent gauge symmetry
• Physics implication from higher weak isospin decomposition
• Tri-hypercharge versus tri-darkcharge
• Questions of flavor physics and neutrino mass from a flipped hypercharge
• Scoto-seesaw model implied by flavor-dependent Abelian gauge charge