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

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.