We present the first complete next-to-next-to-leading order analysis of the Standard Model Higgs potential. We computed the two-loop QCD and Yukawa corrections to the relation between the Higgs quartic coupling (λ) and the Higgs mass (M h ), reducing the theoretical uncertainty in the determination of the critical value of M h for vacuum stability to 1 GeV. While λ at the Planck scale is remarkably close to zero, absolute stability of the Higgs potential is excluded at 98% C.L. for M h < 126 GeV. Possible consequences of the near vanishing of λ at the Planck scale, including speculations about the role of the Higgs field during inflation, are discussed.
The study of the hydrodynamics of bubble growth in first-order phase transitions is very relevant for electroweak baryogenesis, as the baryon asymmetry depends sensitively on the bubble wall velocity, and also for predicting the size of the gravity wave signal resulting from bubble collisions, which depends on both the bubble wall velocity and the plasma fluid velocity. We perform such study in different bubble expansion regimes, namely deflagrations, detonations, hybrids (steady states) and runaway solutions (accelerating wall), without relying on a specific particle physics model. We compute the efficiency of the transfer of vacuum energy to the bubble wall and the plasma in all regimes. We clarify the condition determining the runaway regime and stress that in most models of strong first-order phase transitions this will modify expectations for the gravity wave signal. Indeed, in this case, most of the kinetic energy is concentrated in the wall and almost no turbulent fluid motions are expected since the surrounding fluid is kept mostly at rest.
We propose, for the computation of the Higgs mass spectrum and couplings, a renormalization-group improved leading-log approximation, where the renormalization scale is fixed to the top-quark pole mass. For the case m A ∼ M SUSY , our leading-log approximation differs by less than 2 GeV from previous results on the Higgs mass computed using a nearly scale independent renormalization-group improved effective potential up to nextto-leading order. Moreover, for the general case m A < ∼ M SUSY , we provide analytical formulae (including two-loop leading-log corrections) for all the masses and couplings in the Higgs sector. For M SUSY < ∼ 1.5 TeV and arbitrary values of m A , tan β and the stop mixing parameters, they reproduce the numerical renormalization-group improved leading-log result for the Higgs masses with an error of less than 3 GeV. For the Higgs couplings, our analytical formulae reproduce the numerical results equally well. Comparison with other methods is also performed.
We update instability and metastability bounds of the Standard Model electroweak vacuum in view of the recent ATLAS and CMS Higgs results. For a Higgs mass in the range 124-126 GeV, and for the current central values of the top mass and strong coupling constant, the Higgs potential develops an instability around 10(11) GeV, with a lifetime much longer than the age of the Universe. However, taking into account theoretical and experimental errors, stability up to the Planck scale cannot be excluded. Stability at finite temperature implies an upper bound on the reheat temperature after inflation, which depends critically on the precise values of the Higgs and top masses. A Higgs mass in the range 124-126 GeV is compatible with very high values of the reheating temperature, without conflict with mechanisms of baryogenesis such as leptogenesis. We derive an upper bound on the mass of heavy right-handed neutrinos by requiring that their Yukawa couplings do not destabilize the Higgs potential. (C) 2012 Elsevier B.V. All rights reserved
We assume the validity of the Standard Model up to an arbitrary high-energy scale and discuss what information on the early stages of the Universe can be extracted from a measurement of the Higgs mass. For M h < ∼ 130 GeV, the Higgs potential can develop an instability at large field values. From the absence of excessive thermal Higgs field fluctuations we derive a bound on the reheat temperature after inflation as a function of the Higgs and top masses. Then we discuss the interplay between the quantum Higgs fluctuations generated during the primordial stage of inflation and the cosmological perturbations, in the context of landscape scenarios in which the inflationary parameters scan. We show that, within the large-field models of inflation, it is highly improbable to obtain the observed cosmological perturbations in a Universe with a light Higgs. Moreover, independently of the inflationary model, the detection of primordial tensor perturbations through the B-mode of CMB polarization and the discovery of a light Higgs can simultaneously occur only with exponentially small probability, unless there is new physics beyond the Standard Model.
We critically examine the recent claim that the Standard Model Higgs boson H could drive inflation in agreement with observations if |H| 2 has a strong coupling ξ ∼ 10 4 to the Ricci curvature scalar. We first show that the effective theory approach upon which that claim is based ceases to be valid beyond a cutoff scale Λ = m p /ξ, where m p is the reduced Planck mass. We then argue that knowing the Higgs potential profile for the field values relevant for inflation (|H| > m p / √ ξ ≫ Λ) requires knowledge of the ultraviolet completion of the SM beyond Λ. In absence of such microscopic theory, the extrapolation of the pure SM potential beyond Λ is unwarranted and the scenario is akin to other ad-hoc inflaton potentials afflicted with significant fine-tuning. The appealing naturalness of this minimal proposal is therefore lost.
The Standard Model Higgs potential becomes unstable at large field values. After clarifying the issue of gauge dependence of the effective potential, we study the cosmological evolution of the Higgs field in presence of this instability throughout inflation, reheating and the present epoch. We conclude that anti-de Sitter patches in which the Higgs field lies at its true vacuum are lethal for our universe. From this result, we derive upper bounds on the Hubble constant during inflation, which depend on the reheating temperature and on the Higgs coupling to the scalar curvature or to the inflaton. Finally we study how a speculative link between Higgs meta-stability and consistence of quantum gravity leads to a sharp prediction for the Higgs and top masses, which is consistent with measured values.
It is well known that the electroweak phase transition (EWPhT) in extensions of the Standard Model with one real scalar singlet can be first-order for realistic values of the Higgs mass. We revisit this scenario with the most general renormalizable scalar potential systematically identifying all regions in parameter space that develop, due to tree-level dynamics, a potential barrier at the critical temperature that is strong enough to avoid sphaleron wash-out of the baryon asymmetry. Such strong EWPhTs allow for a simple mean-field approximation and an analytic treatment of the free-energy that leads to very good theoretical control and understanding of the different mechanisms that can make the transition strong. We identify a new realization of such mechanism, based on a flat direction developing at the critical temperature, which could operate in other models. Finally, we discuss in detail some special cases of the model performing a numerical calculation of the one-loop free-energy that improves over the mean-field approximation and confirms the analytical expectations. One-loop Numerical AnalysisSo far, we have identified choices for the T = 0 parameters that lead to strong electroweak phase transitions in the mean-field approximation. It is straightforward to refine these results starting from the same tree-level parameters but including in the scalar potential one-loop T = 0 corrections and the full one-loop thermal integrals (which correctly take into account Boltzmann decoupling effects) further improved by daisy resummation. Details of this standard procedure are given in Appendix A. To illustrate the impact of this refinement, we show in Fig. 9 the ratio v c /T c in the mean-field approximation (blue dashed line) compared with
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