Three-loop \beta-functions for top-Yukawa and the Higgs self-interaction in the Standard Model

TL;DR

This paper analytically computes three-loop -functions for key couplings in the Standard Model, providing precise insights into their quantum corrections and running behaviors.

Contribution

It presents the first detailed three-loop calculations of -functions for the top-Yukawa, strong, and Higgs self-couplings in the unbroken phase of the Standard Model.

Findings

Dominant QCD and top-Yukawa corrections calculated at three-loop level.

Higgs self-interaction effects are negligible for top-Yukawa and strong couplings.

Higgs self-coupling running is significantly affected by Higgs self-interaction contributions.

Abstract

We analytically compute the dominant contributions to the \beta-functions for the top-Yukawa coupling, the strong coupling and the Higgs self-coupling as well as the anomalous dimensions of the scalar, gluon and quark fields in the unbroken phase of the Standard Model at three-loop level. These are mainly the QCD and top-Yukawa corrections. The contributions from the Higgs self-interaction which are negligible for the running of the top-Yukawa and the strong coupling but important for the running of the Higgs self-coupling are also evaluated.