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 beta-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 gamma(5) contribution at order y(t)(4)g(s)(4), a feature not encountered in lower loop orders. We discuss the treatment of gamma(5) which is more involved than in previous calculations at three-loop level.