A Note on Proton Stability in the Standard Model

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 $2N_c{N}_g$. 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.

Comments: Three pages. I suspect this is known to some experts, but I think such an important result deserves to have an accessible explanation available and to be more widely-known. v2: Minor text edits to match published version