Higgs mass implications on the stability of the electroweak vacuum

Joan Elias-Miró,José R Espinosa,Gian F Giudice,Gino Isidori,Antonio Riotto,Alessandro Strumia

doi:10.1016/j.physletb.2012.02.013

Abstract

We update instability and metastability bounds of the Standard Model electroweak vacuum in view of the recent ATLAS and CMS Higgs results. For a Higgs mass in the range 124–126 GeV, and for the current central values of the top mass and strong coupling constant, the Higgs potential develops an instability around 1011 GeV, with a lifetime much longer than the age of the Universe. However, taking into account theoretical and experimental errors, stability up to the Planck scale cannot be excluded. Stability at finite temperature implies an upper bound on the reheat temperature after inflation, which depends critically on the precise values of the Higgs and top masses. A Higgs mass in the range 124–126 GeV is compatible with very high values of the reheating temperature, without conflict with mechanisms of baryogenesis such as leptogenesis. We derive an upper bound on the mass of heavy right-handed neutrinos by requiring that their Yukawa couplings do not destabilize the Higgs potential.

Highlights

Experimental data recently reported by the LHC experiments after the analysis of their 5/fb dataset restrict the Standard Model (SM) Higgs boson mass to be in the range 115 GeV < mh < 131 GeV (ATLAS [1]) and mh < 127 GeV (CMS [2]), with a first hint in the mass window 124 GeV < mh < 126 GeV
Despite the fact that there is no evidence for physics beyond the Standard Model (SM) from the LHC, the experimental information on the Higgs mass gives us useful hints on the structure of the theory at very short distances, thanks to the sizable logarithmic variation of the Higgs quartic coupling at high energies
On any consideration of leptogenesis or reheating temperature, the requirement that the electroweak vacuum has a lifetime longer than the age of the Universe implies an interesting upper bound on the mass of the RH neutrinos, as a function of the physical neutrino mass

Summary

Introduction

Experimental data recently reported by the LHC experiments after the analysis of their 5/fb dataset restrict the Standard Model (SM) Higgs boson mass to be in the range 115 GeV < mh < 131 GeV (ATLAS [1]) and mh < 127 GeV (CMS [2]), with a first hint in the mass window 124 GeV < mh < 126 GeV. If the Universe spent a period of its evolution in the presence of a hot thermal plasma, the absence of excessive thermal Higgs field fluctuations, which might destabilize our present vacuum, imposes an upper bound on the reheat temperature after inflation, generically denoted by TRH. On any consideration of leptogenesis or reheating temperature, the requirement that the electroweak vacuum has a lifetime longer than the age of the Universe implies an interesting upper bound on the mass of the RH neutrinos, as a function of the physical neutrino mass We derive this limit assuming that the SM and the RH neutrinos describe all the degrees of freedom up to a very large energy scale, close to the Planck mass. 0.06 102 104 106 108 1010 1012 1014 1016 1018 1020 RGE scale Μ in GeV mh 126 GeV

Stability and metastability bounds

Meta-stability

Bounds on right-handed neutrinos

Thermal vacuum decay

Thermal vacuum decay and leptogenesis

Conclusions