Two-loop renormalisation of the quark fields in the presence of four-fermion SMEFT operators

TL;DR

This paper calculates two-loop renormalisation constants for quark fields and masses in the Standard Model Effective Field Theory with four-fermion operators, providing results in multiple schemes to aid future precision QCD studies.

Contribution

It provides the first comprehensive two-loop renormalisation constants for quark fields and masses in SMEFT with four-fermion operators, including scheme dependence analysis.

Findings

Results in NDR and BMHV schemes for all relevant constants.

Completes the set of renormalisation constants needed for two-loop SMEFT QCD calculations.

Facilitates more precise theoretical predictions involving SMEFT operators.

Abstract

We compute the contributions of the dimension-6 SMEFT operators involving four third-generation quarks to the two-loop renormalisation of the quark fields and masses. We perform the computations in both the Naive Dimensional Regularisation (NDR) and the Breitenlohner-Maison-`t Hooft-Veltman (BMHV) schemes, and we present results for all relevant field and mass renormalisation constants in the on-shell and MS-bar schemes. We carefully discuss all scheme choices which affect the final results. This completes the computation of field and mass renormalisation constants relevant for two-loop computations in QCD involving dimension-six SMEFT operators.