The top quark and Higgs boson masses and the stability of the electroweak vacuum

S Alekhin,A Djouadi,S Moch

doi:10.1016/j.physletb.2012.08.024

Abstract

The ATLAS and CMS experiments observed a particle at the LHC with a mass ≈126 GeV, which is compatible with the Higgs boson of the Standard Model. A crucial question is, if for such a Higgs mass value, one could extrapolate the model up to high scales while keeping the minimum of the scalar potential that breaks the electroweak symmetry stable. Vacuum stability requires indeed the Higgs boson mass to be MH≳129±1 GeV, but the precise value depends critically on the input top quark pole mass which is usually taken to be the one measured at the Tevatron, mtexp=173.2±0.9 GeV. However, for an unambiguous and theoretically well-defined determination of the top quark mass one should rather use the total cross section for top quark pair production at hadron colliders. Confronting the latest predictions of the inclusive pp¯→tt¯+X cross section up to next-to-next-to-leading order in QCD to the experimental measurement at the Tevatron, we determine the running mass in the MS¯-scheme to be mtMS¯(mt)=163.3±2.7 GeV which gives a top quark pole mass of mtpole=173.3±2.8 GeV. This leads to the vacuum stability constraint MH⩾129.4±5.6 GeV to which a ≈126 GeV Higgs boson complies as the uncertainty is large. A very precise assessment of the stability of the electroweak vacuum can only be made at a future high-energy electron–positron collider, where the top quark pole mass could be determined with a few hundred MeV accuracy.

Highlights

The ATLAS and CMS experiments observed a particle at the Large Hadron Collider (LHC) with a mass ≈ 126 GeV, which is compatible with the Higgs boson of the Standard Model
The recent results on Higgs boson searches delivered by the ATLAS and CMS collaborations [1] at the Large Hadron Collider (LHC) show that there is an established signal corresponding to a particle with a mass ≈ 126 GeV and with the properties expected for the Standard Model (SM) Higgs boson [2, 3]
This full NNLO calculation is based on three main ingredients that have been calculated only very recently: the two-loop threshold corrections to the quartic coupling λ at the weak scale, λ(μ) = MH2 /2v2 + ∆λ(μ) which involve the QCD and the Yukawa interactions [6, 7], the three-loop leading contributions to the renormalization group evolution of the coupling λ as well as the top quark Yukawa coupling and the Higgs mass anomalous dimension [8], and the three-loop corrections to the beta functions of the three SM gauge couplings taking into account Yukawa and Higgs self couplings [9]