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 γ 5 contribution at order y 4 g 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.