Renormalization group evolution of dimension-six baryon number violating operators

TL;DR

The paper provides a complete one-loop calculation of the anomalous-dimension matrix for the dimension-six baryon-number-violating operators in the SM EFT, explicitly including right-handed neutrinos and their Majorana mass. It decomposes the RGEs into gauge and Yukawa contributions and organizes the flavor structure by permutation representations, confirming gauge terms are diagonal in this basis and enumerating a total of $408$ independent $\Delta B=1$ operators. The analysis also explores flavor-symmetry implications, showing naive Minimal Flavor Violation cannot apply to these operators, but a Grand Unified Theory–inspired MFV framework is possible, with Yukawa corrections generally smaller than gauge effects. Numerically, gauge running dominates the evolution from the GUT to the electroweak scale, with Yukawa effects providing only modest corrections, except potentially for heavy-flavor BNV where two-loop mixing becomes relevant. These results complete the one-loop RG evolution for all SM dimension-six operators and provide a basis for robust BNV phenomenology in MFV and GUT contexts.

Abstract

We calculate the one-loop anomalous dimension matrix for the dimension-six baryon number violating operators of the Standard Model effective field theory, including right-handed neutrino fields. We discuss the flavor structure of the renormalization group evolution in the contexts of minimal flavor violation and unification.

Figures (1)

• Figure 1: The one-loop Yukawa renormalization graph.