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We investigate the role of anomalous gauge boson and fermion couplings on theproduction of $WZ$ and $W^+W^-$ pairs at the LHC to NLO QCD in the StandardModel effective field theory, including dimension-6 operators. Our results areimplemented in a publicly available version of the POWHEG-BOX. We combine our$WZ$ results in the leptonic final state $e\nu \mu^+\mu^-$ with previous$W^+W^-$ results to demonstrate the numerical effects of NLO QCD corrections onthe limits on effective couplings derived from ATLAS and CMS 8 and 13 TeVdifferential measurements. Our study demonstrates the importance of includingNLO QCD SMEFT corrections in the $WZ$ analysis, while the effects on $WW$production are smaller. We also show that the $\mathcal{O}(1/\Lambda^4)$contributions dominate the analysis, where $\Lambda$ is the high energy scaleassociated with the SMEFT.

QCD Corrections in SMEFT Fits to $WZ$ and $WW$ Production