Baryon Number, Lepton Number, and Operator Dimension in the Standard Model

TL;DR

This paper proves a fundamental relation between operator dimension and baryon and lepton numbers in the Standard Model, confirming long-held expectations with a rigorous demonstration that holds even with added right-handed neutrinos.

Contribution

It provides a rigorous proof linking operator dimension parity to baryon and lepton number differences in the Standard Model, including extensions with right-handed neutrinos.

Findings

Operators with B-L=0 are of even dimension

B-L must be an even number

Results hold with added right-handed neutrinos

Abstract

We prove that for a given operator in the Standard Model (SM) with baryon number B and lepton number L, that the operator's dimension is even (odd) if (B-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 B-L=0 are of even dimension, B-L must be an even number, etc. These results remain true even if the SM is augmented by any number of right-handed neutrinos with L=1.