Vacuum stability in the SM and the three-loop \beta-function for the Higgs self-interaction

TL;DR

This paper examines the stability of the Standard Model vacuum considering radiative corrections, focusing on the Higgs self-interaction's evolution via a newly computed three-loop beta function, highlighting uncertainties mainly from the top quark mass.

Contribution

The paper provides an analytical calculation of the dominant three-loop contributions to the Higgs self-interaction beta function, enhancing understanding of vacuum stability at high energies.

Findings

The three-loop beta function includes significant QCD and top-Yukawa corrections.

Vacuum stability depends critically on the Higgs and top quark masses.

Uncertainties in top quark mass prevent definitive conclusions on stability.

Abstract

In this article the stability of the Standard Model (SM) vacuum in the presence of radiative corrections and for a Higgs boson with a mass in the vicinity of 125 GeV is discussed. The central piece in this discussion will be the Higgs self-interaction $\lambda$ and its evolution with the energy scale of a given physical process. This is described by the $\beta$-function to which we recently computed analytically the dominant three-loop contributions. These are mainly the QCD and top-Yukawa corrections as well as the contributions from the Higgs self-interaction itself. We will see that for a Higgs boson with a mass of about 125 GeV the question whether the SM vacuum is stable and therefore whether the SM could be valid up to Planck scale cannot be answered with certainty due to large experimental uncertainties, mainly in the top quark mass.