On two-loop corrections to the Higgs trilinear coupling in models with extended scalar sectors

Johannes Braathen,Shinya Kanemura

doi:10.1016/j.physletb.2019.07.021

Abstract

We investigate the possible size of two-loop radiative corrections to the Higgs trilinear coupling λhhh in two types of models with extended Higgs sectors, namely in a Two-Higgs-Doublet Model (2HDM) and in the Inert Doublet Model (IDM). We calculate the leading contributions at two loops arising from the additional (heavy) scalars and the top quark of these theories in the effective-potential approximation. We include all necessary conversion shifts in order to obtain expressions both in the MS‾ and on-shell renormalisation schemes, and in particular, we devise a consistent “on-shell” prescription for the soft-breaking mass of the 2HDM at the two-loop level. We illustrate our analytical results with numerical studies of simple aligned scenarios and show that the two-loop corrections to λhhh remain smaller than their one-loop counterparts, with a typical size being 10−20% of the one-loop corrections, at least while perturbative unitarity conditions are fulfilled. As a consequence, the existence of a large deviation of the Higgs trilinear coupling from the prediction in the Standard Model, which has been discussed in the literature at one loop, is not altered significantly.

Highlights

The discovery of the 125-GeV Higgs boson at the CERN LHC in 2012 has been a great success for particle physics, and has completed the particle spectrum of the Standard Model (SM)
While it is established that the Higgs sector is responsible for the electroweak symmetry breaking (EWSB), very little is known about the nature of the Higgs potential – only its minimum and the curvature around the minimum are known
If we consider the size of the BSM deviations for MΦ = 300 GeV and 400 GeV, we find that two-loop corrections are respectively about 10% and 20% of their one-loop counterparts

Summary

INTRODUCTION

The discovery of the 125-GeV Higgs boson at the CERN LHC in 2012 has been a great success for particle physics, and has completed the particle spectrum of the Standard Model (SM). A first possible explanation for this could be that new physics only exists beyond the scale currently accessible at colliders, and their effects would be (almost) impossible to find Another interesting possibility would be that the new states are made somehow difficult to observe via some symmetry or mechanism. Non-decoupling effects are common in these one-loop calculations, thereby posing the question of whether new large corrections can occur at two loops. While the new two-loop contributions remain well under control (at least while perturbative unitarity is maintained) and do not significantly alter the non-decoupling effects found at one loop, they turn out not to be entirely negligible either

THE TWO-HIGGS-DOUBLET MODEL

ONE-LOOP CORRECTIONS TO λhhh AND NON-DECOUPLING EFFECTS

TWO-LOOP CORRECTIONS TO λhhh AND NUMERICAL ANALYSIS

Findings

CONCLUSION