${\gamma }_5$ schemes and the interplay of SMEFT operators in the Higgs-gluon coupling

We calculate the four-top-quark operator contributions to Higgs production via gluon fusion in the Standard Model effective field theory. The four-top operators enter for the first time via two-loop diagrams. Owing to their chiral structure they contain ${\gamma }_5$, so special care needs to be taken when using dimensional regularization for the loop integrals. We use two different schemes for the continuation of ${\gamma }_5$ to $D$ space-time dimensions in our calculations and present a mapping for the parameters in the two schemes. This generically leads to an interplay of different operators, such as four-top operators, chromomagnetic operators, or Yukawa-type operators at the loop level. We validate our results by examples of matching onto UV models.