Top-Yukawa effects on the β-function of the strong coupling in the SM at four-loop level

We present analytical results for the QCD β-function extended to the gaugeless limit of the unbroken phase of the Standard Model at four-loop level. Apart from the strong coupling itself we include the top-Yukawa contribution and the Higgs self-coupling. We observe a numerically small non-naive γ₅ contribution at order y t 4 g s 4 , a feature not encountered in lower loop orders. We discuss the treatment of γ₅ which is more involved than in previous calculations at three-loop level