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

Abstract

The ATLAS and CMS experiments observed a particle at the LHC with a mass $\approx 126$ 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 $M_H \gsim 129 \pm 1$ 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, $m_t^{\exp }=173.2\pm 0.9$ 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 $p\bar{p}\to t\bar{t}+X$ 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 $\overline{\mathrm{MS}}$-scheme to be $m_t^{\overline{\mathrm{MS}}}(m_t)=163.3\pm 2.7$ GeV which gives a top quark pole mass of $m_t^{\mathrm{pole}}=173.3\pm 2.8$ GeV. This leads to the vacuum stability constraint $M_H\ge 129.8\pm 5.6$ GeV to which a $\approx 126$ 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.

12 pages, 1 figure. v2: lapsus corrected in the abstract. v3: typos corrected, updated (and 2 figures added) with most recent data

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• Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC
• Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC
• Parton distributions for the LHC
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• Theoretical status and prospects for top-quark pair production at hadron colliders
• Measuring the running top-quark mass
• Next-to-next-to-leading soft-gluon corrections for the top quark cross section and transverse momentum distribution
• The Probable Fate of the Standard Model
• Non-perturbative QCD Effects and the Top Mass at the Tevatron
• Electroweak effects in top-quark pair production at Hadron Colliders
• Top Mass Measurements from Jets and the Tevatron Top-Quark Mass
• Weak interaction corrections to hadronic top quark pair production
• Top-quark pair production near threshold at LHC
• Bound-state Effects on Top Quark Production at Hadron Colliders
• Inclusive top-pair production phenomenology with TOPIXS
• Combination of CDF and DO results on the mass of the top quark using up to 8.7 fb^{-1} at the Tevatron
• Top-quark processes at NLO in production and decay
• NNNLO results on top-quark pair production near threshold
• Top-quark mass measurements at the LHC
• Top-quark pair-production with one jet and parton showering at hadron colliders

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