We study the effects of the one-loop renormalisation group running/mixing of the Wilson coefficients in the standard model effective field theory on the predictions for Hj, \( t\overline{t}H \) and HH production at the LHC. We focus on a subset of operators closed under QCD corrections and explore the differences between employing a fixed or dynamical scale on the SMEFT predictions for key observables such as the Higgs transverse momentum and the Higgs pair invariant mass. We then study the impact of consistently taking into account renormalisation group effects on the constraints that can be obtained on the Wilson coefficients through current and future measurements at the LHC.
