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

TL;DR

This paper provides four-loop analytical calculations of the QCD $eta$-function within the Standard Model, incorporating top-Yukawa and Higgs self-coupling effects, revealing novel $ ext{γ}_5$ contributions at higher order.

Contribution

It extends the QCD $eta$-function calculation to four loops in the Standard Model, including top-Yukawa and Higgs couplings, and uncovers new $ ext{γ}_5$ effects at this order.

Findings

Four-loop $eta$-function results for the Standard Model.

Identification of non-naive $ ext{γ}_5$ contributions at order $y_t^4 g_s^4$.

Enhanced understanding of high-order corrections in SM coupling evolution.

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.