A Note on Proton Stability in the Standard Model

TL;DR

This paper identifies a specific global symmetry in the Standard Model that guarantees proton stability nonperturbatively, highlighting its importance and noting that many beyond Standard Model theories break this symmetry.

Contribution

It reveals an exact, anomaly-free global symmetry in the Standard Model responsible for proton stability, which is often overlooked in beyond Standard Model theories.

Findings

Standard Model has an exact global symmetry ensuring proton stability.

This symmetry is anomaly-free and generation-independent.

Many beyond Standard Model theories break this symmetry.

Abstract

In this short note we describe the symmetry responsible for absolute, nonperturbative proton stability in the Standard Model. The SM with $N_c$ colors and ${N_g}$ generations has an exact, anomaly-free, generation-independent, global symmetry group $U(1)_{B-N_c L} \times \mathbb{Z}_{N_g}^L$, which contains a subgroup of baryon plus lepton number of order $2 N_c {N_g}$. This disallows proton decay for ${N_g}>1$. Many well-studied models beyond the SM explicitly break this global symmetry, and the alternative deserves further attention.