Beyond $\boldsymbol{SU(N)}$: $\boldsymbol{U(3) \times U(2)}$ as the underlying symmetry of the strong and electroweak interactions

TL;DR

This paper proposes a novel gauge framework based on local U(3)×U(2) symmetry, which naturally explains features of the Standard Model and suggests a new underlying symmetry for strong and electroweak interactions.

Contribution

It extends the gauge principle to promote all SU(N) symmetries to U(N), providing a unified model that predicts charge quantization, hypercharge assignments, and neutrino masses.

Findings

Charge quantization emerges naturally.

Hypercharge assignments are uniquely predicted.

Neutrino masses are explained via an additional U(1) factor.

Abstract

The gauge principle is a cornerstone of particle-physics model building. Nevertheless, many constructions leave certain global $U(1)$ redundancies ungauged. In this work, we take the gauge principle to its logical extreme by promoting all $SU(N)$ symmetries to $U(N)$. We focus on a model based on local $U(3)\times U(2)$ invariance. This framework accounts for several otherwise ad hoc features of the Standard Model, including charge quantization and the observed hypercharge assignments, which emerge here as unique predictions. Furthermore, the internal consistency of the model requires the introduction of right-handed neutrinos and implies the presence of an additional $U(1)$ factor that can be identified with $B-L$, thereby naturally yielding non-zero neutrino masses. In light of these findings, we hypothesize that $U(3)\times U(2)$ constitutes the underlying symmetry of the strong and electroweak interactions. More importantly, our approach opens up novel avenues for model building, driven by this extended interpretation of the gauge principle.