Two loops, four tops and two $γ_5$ schemes: a renormalization story

We calculate the four-top quark operator contributions to the two-loop renormalization constants of the fermion and gluon fields, necessary to obtain the renormalization group equations for the fermion masses and the strong coupling constant. The computation has been carried out in the na\"ıve dimensional regularization scheme for the $γ_5$ matrix. We also discuss a strategy to translate the results into the Breitenlohner--Maison--'t~Hooft--Veltman scheme and present the corresponding beta functions in both schemes.