Two-loop running effects in Higgs physics in Standard Model Effective Field Theory

We consider the renormalization group equations within the Standard Model Effective Field Theory and compute two-loop contributions proportional to the top quark Yukawa coupling for the operator generating an effective Higgs-gluon coupling, focusing on the Yukawa-like operator. These two-loop running effects are relevant for processes where the effective Higgs-gluon coupling contributes at a lower loop order compared to the Standard Model contribution and where a dynamical scale choice is adopted. Such a situation arises, for instance, in the Higgs transverse momentum distribution and Higgs pair production. We investigate the phenomenological impact of our computations on these two processes and find that the two-loop contributions are significant and can lead to deviations of up to 20% in the scenarios we consider.