Stability of the Electroweak Vacuum: Gauge Independence and Advanced Precision

Abstract

We perform a manifestly gauge-independent analysis of the vacuum stability in the standard model including two-loop matching, three-loop renormalization group evolution, and pure QCD corrections through four loops. All these ingredients are exact, except that light-fermion masses are neglected. We in turn apply the criterion of nullifying the Higgs self-coupling and its beta function in the modified minimal-subtraction scheme and a recently proposed consistent method for determining the true minimum of the effective Higgs potential that also avoids gauge dependence. Exploiting our knowledge of the Higgs-boson mass, we derive an upper bound on the pole mass of the top quark by requiring that the standard model be stable all the way up to the Planck mass scale and conservatively estimate the theoretical uncertainty. This bound is compatible with the Monte Carlo mass quoted by the Particle Data Group at the 1.3σ level.PACS numbers: 11.10. Gh,11.10.Hi,14.65.Ha,14.80.Bn The standard model (SM) of elementary particle physics has been enormously consolidated by the discovery [1] at the CERN Large Hadron Collider of a new weak neutral resonance that, within the present experimental uncertainty, shares the spin (J), parity (P ), and charge-conjugation (C) quantum numbers J P C = 0 ++ and the coupling strengths with the SM Higgs boson H, in the absence of convincing signals of new physics beyond the SM. Moreover, its mass of (125.7 ± 0.4) GeV [2] falls well inside the M H range predicted within the SM through global analyses of electroweak (EW) precision data [2]. Besides completing the SM particle multiplet and confirming the Higgs mechanism of mass generation via the spontaneous breaking of the EW symmetry proposed by Englert, Higgs (The Nobel Prize in Physics 2013), and Brout, this groundbreaking discovery also has fundamental cosmological consequences by allowing conclusions regarding the fate of the Universe via the analysis of the vacuum stability [3]. In fact, owing to an intriguing conspiracy of the SM particle masses, chances are that the Higgs potential develops a second minimum, as deep as the one corresponding to the vacuum with expectation value (VEV) v = 2 −1/4 G −1/2 F = 246 GeV in which we live, at a field value of the order of the Planck mass M P = 1.22 × 1019 GeV [4,5]. This would imply that the SM be stable all the way up to the energy scale where the unification with gravity is expected to take place anyways, which would diminish the necessity for grand unified theories at lower scales. EW symmetry breaking might thus be determined by Planck-scale physics [5], and the existence of a relationship between M P and SM parameters might signify a reduction of fundamental couplings. Of course, experimental facts that the SM fails to explain, such as the smallness of the neutrino masses, the strong CP problem, the existence of dark matter, and the baryon asymmetry in the Universe, would then still call for an extension.Obviously, the ultimate answer to the existential question whether our vacuum is stable o...

Triple Higgs boson production at a 100 TeV proton-proton collider

“…6 We have verified explicitly that an alternative method based on minimization of the squared sum of (m bb − m h ) from each combination yields results that differ by O(1%) compared to the simpler ∆R method. 7 The distance between the other paired b-jets was not found to have significant discriminatory power. 8 This cut implies that the di-photon resolution should be better than ∼ 1 GeV at the FCC-hh.…”

“…The so-called 'self-couplings' and their energy dependence are crucial in determining the stability of the vacuum. Current observations suggest that our Universe may be sitting at a metastable false vacuum [1][2][3][4][5][6][7][8] and measurements of these couplings will illuminate this fact further. At colliders, these terms, i.e.…”

“…6 We thus construct the paired b-jet invariant mass, respectively, m . 7 For the photon pair, we simply construct the invariant mass and impose a strong window on the measured Higgs boson mass m γγ ∈ [124, 126] GeV. 8 We also restrict the distance between the two photons to ∆R γγ ∈ [0.2, 4.0].…”

Semiclassical description of soliton-antisoliton pair production in particle collisions

“…Although these processes occur with exponentially small rates [14][15][16][17][18][19][20][21][22][23][24][25] in weakly interacting theories, they may be important for baryogenesis [8,26,27], stability of the Higgs vacuum [28][29][30][31][32][33][34][35], or violation of the baryon and lepton numbers at future colliders [36][37][38][39]. We consider nonperturbative transitions of a new type: classically forbidden creation of topological soliton-antisoliton pairs in N -particle collisions, see the sketch of the N = 2 process in figures 1a,b.…”

Top Physics at CMS/LHC

“…With the discovery of a Higgs boson at the LHC with a mass of about 126 GeV [22,23], the precision measurement of the top-quark mass takes a central role in the question of the stability of the electroweak vacuum. Recent NNLO calculations [24,25] together with the central values of the Higgs and top-quark masses put the electroweak vacuum in the metastable region. The uncertainty is dominated by the precision of the top-quark mass measurement and its interpretation as the pole mass.…”