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 $2 N_c {N_g}$. 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.