Revisiting the connection of baryon number, lepton number, and operator dimension

TL;DR

This paper refines the theoretical relationship between baryon and lepton number violation and operator dimension in effective field theories, providing improved bounds and explicit constructions up to high dimensions.

Contribution

It derives an improved inequality linking baryon/lepton number to operator dimension and shows this relationship becomes an equality at high dimensions in the Standard Model with right-handed neutrinos.

Findings

Derived a new inequality connecting operator dimension with baryon and lepton number.

Compared the inequality with explicit operators up to dimension 25.

Established that the relationship becomes an equality at high dimensions for the Standard Model plus right-handed neutrinos.

Abstract

The effects of heavy new particles beyond the Standard Model can be conveniently captured through higher-dimensional effective operators. As noted long ago by Weinberg, the amount of baryon and lepton number an operator can carry is intricately connected to its mass dimension. We derive an improved inequality for this connection and compare it to explicit operator constructions up to mass dimension 25. For the effective field theory of Standard Model plus right-handed neutrinos, our relationship is even an equality up to high mass dimension.