Renormalization Group Evolution from On-shell SMEFT

TL;DR

This paper introduces an efficient on-shell method for deriving the one-loop Renormalization Group evolution of Wilson coefficients in SMEFT, simplifying calculations through amplitude basis and scalar bubble integrals.

Contribution

It presents a novel on-shell approach for calculating RG evolution of Wilson coefficients, including contributions from higher-dimensional operators, improving computational efficiency.

Findings

Derived anomalous dimensions at dimension six.

Calculated contributions from dimension-8 operators.

Provided pedagogical examples of the method.

Abstract

We describe the on-shell method to deriving the Renormalization Group (RG) evolution of Wilson coefficients of high dimensional operators at one loop, which is a necessary part in the on-shell construction of the Standard Model Effective Field Theory (SMEFT), and exceptionally efficient based on the amplitude basis in hand. The UV divergence is obtained by firstly calculating the coefficients of scalar bubble integrals by unitary cuts, then subtracting the IR divergence in the massless bubbles, which can be easily read from the collinear factors we obtained for the Standard Model fields. Examples of deriving the anomalous dimensions at dimension six are presented in a pedagogical manner. We also give the results of contributions from the dimension-8 $H^4D^4$ operators to the running of $V^+V^-H^2$ operators, as well as the running of $B^+B^-H^2D^{2n}$ from $H^4D^{2n+4}$ for general $n$.