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

The ATLAS and CMS experiments observed a particle at the LHC with a mass ≈126GeV, 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±1GeV, 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±0.9GeV. 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±2.7GeV which gives a top quark pole mass of mtpole=173.3±2.8GeV. This leads to the vacuum stability constraint MH⩾129.4±5.6GeV to which a ≈126GeV 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.