Two-loop renormalisation of quark and gluon fields in the SMEFT in the on-shell scheme

TL;DR

This paper calculates two-loop renormalisation constants for quark and gluon fields within the SMEFT framework, focusing on specific operators and their impact on the strong coupling's evolution.

Contribution

It provides the first detailed two-loop renormalisation constants for quark and gluon fields in the SMEFT in the on-shell scheme, including effects of key dimension-six operators.

Findings

Two-loop renormalisation constants for quark and gluon fields computed.

Implications for the running of the strong coupling constant analyzed.

Effects of specific dimension-six operators on renormalisation quantified.

Abstract

We compute the contributions of CP-conserving dimension-six SMEFT operators to the two-loop renormalisation constants of quark and gluon fields in the on-shell scheme. Specifically, we consider the top-quark chromomagnetic operator and the triple gluon operator. We also compute the contribution of four-quark operators to the gluon renormalisation constant and discuss the implications for the running of the strong coupling constant.