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...

We present the results for three-loop beta-functions for Yukawa couplings of heavy Standard Model fermions calculated within the unbroken phase of the model. The calculation is carried out with the help of the MINCER program in a general linear gauge, and the final result is independent of the gauge-fixing parameters. In order to calculate three-point functions, we made use of infrared rearrangement (IRR) trick. Due to the chiral structure of the SM a careful treatment of loops with fermions is required to perform the calculation. It turns out that gauge anomaly cancellation in the SM allows us to obtain the result by means of the semi-naive treatment of gamma5.Comment: 7 pages, 1 figure, discussion about gamma5 extended, numerical estimates changed according to new ancillary files with correct result

We present the results for three-loop beta-function for the Higgs self-coupling calculated within the unbroken phase of the Standard Model. We also provide the expression for three-loop beta-function of the Higgs mass parameter, which is obtained as a by-product of our main calculation. Our results coincide with that of recent paper arXiv:1303.2890. In addition, the expression for the Higgs field anomalous dimension is given.Comment: 15 pages, 1 figure, Mathematica outputs attached. Ancillary files rearranged. arXiv admin note: text overlap with arXiv:1212.682

We study the relationships between the basic parameters of the on-shell renormalization scheme and their counterparts in the $\overline{\mathrm{MS}}$ scheme at full order ${\cal O}(\alpha^2)$ in the Standard Model. These enter as threshold corrections the renormalization group analyses underlying, e.g., the investigation of the vacuum stability. To ensure the gauge invariance of the parameters, in particular of the $\overline{\mathrm{MS}}$ masses, we work in $R_\xi$ gauge and systematically include tadpole contributions. We also consider the gaugeless-limit approximation and compare it with the full two-loop electroweak calculation.Comment: 33 pages, 1 figure, matches journal publicatio