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We provide the complete set of predictions needed to achieve NLO accuracy inthe Standard Model Effective Field Theory at dimension six for Higgs productionin gluon fusion. In particular, we compute for the first time the contributionof the chromomagnetic operator $ \bar Q_L \Phi \sigma q_R G$ at NLO in QCD,which entails two-loop virtual and one-loop real contributions, as well asrenormalisation and mixing with the Yukawa operator $\Phi^\dagger \Phi\, \barQ_L \Phi q_R$ and the gluon-fusion operator $\Phi^\dagger \Phi\, GG$. Focusingon the top-quark-Higgs couplings, we consider the phenomenological impact ofthe NLO corrections in constraining the three relevant operators byimplementing the results into the MadGraph5_aMC@NLO framework. This allows usto compute total cross sections as well as to perform event generation at NLOthat can be directly employed in experimental analyses.

Gluon-fusion Higgs production in the Standard Model Effective Field Theory