Beta-function for the Higgs self-interaction in the Standard Model at three-loop level

TL;DR

This paper presents a three-loop calculation of the Higgs self-interaction beta function in the Standard Model, analyzing its implications for vacuum stability and comparing theoretical precision with experimental uncertainties.

Contribution

It provides the first three-loop beta function for the Higgs self-coupling in the Standard Model, enhancing the precision of vacuum stability analyses.

Findings

Three-loop beta function for Higgs self-interaction calculated.

Improved theoretical precision in vacuum stability predictions.

Comparison of theoretical uncertainties with experimental parameter errors.

Abstract

The discovery of a Higgs particle has triggered numerous theoretical and experimental investigations concerning its production and decay rates and has led to interesting results concerning its interaction with fermions and gauge bosons. The self-interaction $\lambda$ of the Standard Model Higgs boson is particularly important due to its close connection with the stability of the SM vacuum. In this talk precision calculations for the evolution of this crucial coupling are presented and their impact on the question of vacuum stability is analysed. We also compare the theoretical precision resulting from the calculation of three-loop $\beta$-functions to the experimental uncertainties stemming from key parameters, such as the top mass, the Higgs mass and the strong coupling, and to the theoretical uncertainties introduced by the matching of experimental data to parameters in the theoretically favoured $\overline{\text{MS}}$ renormalization scheme.