  We explore the impact of Renormalisation Group (RG) effects in the Standard
Model Effective Field Theory (SMEFT) interpretations of LHC measurements. We
implement the RG running and mixing for the Wilson coefficients as obtained
from the one-loop anomalous dimension matrix in the SMEFT into a Monte Carlo
generator. This allows to consistently predict and combine in global fits
collider observables characterised by different scales. As a showcase, we
examine the impact of RG running in the strong coupling on the SMEFT
predictions for $t \bar t$ production cross sections and differential
distributions as well as on the bounds on the Wilson coefficients that can be
obtained from current LHC data.
