Next-to-Leading Order Running in the SMEFT

TL;DR

This paper derives the two-loop renormalization group equations for the baryon-number-conserving sector of the dimension-six SMEFT, enabling more precise NLO calculations and operator mixing analysis.

Contribution

It presents the first two-loop order renormalization group equations for the SMEFT's baryon-number-conserving sector, using functional methods and addressing scheme ambiguities.

Findings

Two-loop SMEFT RG equations are now available.

Strategies to mitigate reading-point ambiguities are developed.

Results are provided for practical implementation.

Abstract

The next-to-leading order (NLO) Standard Model Effective Field Theory (SMEFT) renormalization group equations are needed to account for phenomenologically relevant operator mixing and ensure renormalization scale independence in NLO calculations of observables. For the first time, we present the renormalization group equations of the baryon-number-conserving sector of the dimension-six SMEFT up to two-loop order. Our calculations have been performed using functional methods with an anticommuting $ \gamma_5 $-scheme. A variety of strategies are employed to mitigate the reading-point ambiguities inherent to this scheme choice. We also describe how a local version of the $ \boldsymbol{R}^\ast $-method is adapted to handle the evanescent operators arising in dimensional regularization. The results are provided in various supplementary files to make them accessible for both human inspection and numerical implementation.