Renormalization-group equations of the LEFT at two loops: dimension-six baryon-number-violating operators

TL;DR

This paper calculates the two-loop anomalous dimensions for dimension-six baryon-number-violating operators in the low-energy effective field theory below the electroweak scale, aiding precision studies of proton decay constraints.

Contribution

It provides the first comprehensive two-loop anomalous dimension calculations for baryon-number-violating operators in the LEFT, using two different regularization schemes.

Findings

Results in 't Hooft-Veltman scheme with finite renormalizations

Results in naive dimensional regularization without ill-defined traces

Facilitates more accurate proton decay constraint analysis

Abstract

We present the second part of a systematic calculation of the two-loop anomalous dimensions for the low-energy effective field theory below the electroweak scale (LEFT): the baryon-number-violating sector at dimension six in the power counting. We obtain the results in two different schemes: in the algebraically consistent 't Hooft-Veltman scheme for $\gamma_5$, corrected for evanescent as well as chiral-symmetry-breaking effects through finite renormalizations; and in naive dimensional regularization, which in the considered sector of the theory does not lead to any ill-defined $\gamma_5$-odd traces. Our results are of interest for a reanalysis of the constraints on physics beyond the Standard Model from proton-decay searches within an EFT framework at next-to-leading-logarithmic accuracy.