Baryon number, lepton number, and operator dimension in the Standard Model

Abstract

We prove that for a given operator in the Standard Model (SM) with baryon number ΔB and lepton number ΔL, that the operator's dimension is even (odd) if (ΔB−ΔL)/2 is even (odd). Consequently, this establishes the veracity of statements that were long observed or expected to be true, but not proven, e.g., operators with ΔB−ΔL=0 are of even dimension, ΔB−ΔL must be an even number, etc. These results remain true even if the SM is augmented by any number of right-handed neutrinos with ΔL=1.