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

We prove that for a given operator in the Standard Model (SM) with baryon number AB and lepton number AL, that the operator's dimension is even (odd) if (AB - Delta L)/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 Delta B - Delta L = 0 are of even dimension, AB - AL must be an even number, etc. These results remain true even if the SM is augmented by any number of right-handed neutrinos with Delta L =1. (C) 2016 The Author. Published by Elsevier B.V. This is an open access article under the CC BY license (Imp://creativecommons.orgilicenses/by/4.0/). Funded by SCOAP(3).