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

Abstract

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 non-naive $\gamma_5$ contribution at order $y_t^4 g_s^4$, a feature not encountered in lower loop orders.Comment: v2: more sophisticated treatment and more detailed description of the non-naive \gamma_5 contribution; Ref. added. v3: this the version published in JHEP; references [49,50] fixed; v4: changed statement on p.8: a different gamma_5 treatment only leads to a factor 3, not a factor 6 in the non-naive part compared to the prescription used in this paper. Note added on recent developments (p. 12