Generalized Gauge U(1) Family Symmetry for Quarks and Leptons

TL;DR

This paper explores a class of anomaly-free U(1) gauge symmetries extending the Standard Model with right-handed neutrinos, introducing new models that could be tested at the LHC.

Contribution

It derives a simple anomaly cancellation constraint for U(1) extensions and presents two novel solutions offering insights into fermion mixing.

Findings

Identifies an infinite set of anomaly-free U(1) symmetries with a single constraint.

Proposes two new U(1) models related to fermion mixing.

Suggests potential experimental verification at the LHC.

Abstract

If the standard model of quarks and leptons is extended to include three singlet right-handed neutrinos, then the resulting fermion structure admits an infinite number of anomaly-free solutions with just one simple constraint. Well-known examples satisfying this constraint are $B-L$, $L_{\mu}-L_{\tau}$ , $B-3L_{\tau}$ , etc. We derive this simple constraint, and discuss two new examples which offer some insights to the structure of mixing among quark and lepton families, together with their possible verification at the Large Hadron Collider.