Stability and UV completion of the Standard Model
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Abstract:
The knowledge of the stability condition of the electroweak (EW) vacuum is of the greatest importance for our understanding of beyond Standard Model (BSM) physics. It is widely believed that new physics that lives at very high energy scales should have no impact on the stability analysis. This expectation has been recently challenged, but the results were controversial as new physics was given in terms of non-renormalizable higher order operators. Here we consider for the first time a renormalizable (toy) UV completion of the SM, and definitely show that such a decoupling does not take place. This result has important phenomenological consequences, providing a very useful test for BSM theories. In particular, it shows that speculations based on the so called criticality do not appear to be well founded.Keywords:
Decoupling (probability)
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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.
Cosmological constant
False vacuum
Inflationary epoch
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We investigate the possibility that radiative corrections may produce spontaneous symmetry breakdown in theories for which the semiclassical (tree) approximation does not indicate such breakdown. The simplest model in which this phenomenon occurs is the electrodynamics of massless scalar mesons. We find (for small coupling constants) that this theory more closely resembles the theory with an imaginary mass (the Abelian Higgs model) than one with a positive mass; spontaneous symmetry breaking occurs, and the theory becomes a theory of a massive vector meson and a massive scalar meson. The scalar-to-vector mass ratio is computable as a power series in $e$, the electromagnetic coupling constant. We find, to lowest order, $\frac{{m}^{2}(S)}{{m}^{2}(V)}=(\frac{3}{2\ensuremath{\pi}})(\frac{{e}^{2}}{4\ensuremath{\pi}})$. We extend our analysis to non-Abelian gauge theories, and find qualitatively similar results. Our methods are also applicable to theories in which the tree approximation indicates the occurrence of spontaneous symmetry breakdown, but does not give complete information about its character. (This typically occurs when the scalar-meson part of the Lagrangian admits a greater symmetry group than the total Lagrangian.) We indicate how to use our methods in these cases.
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We consider the renormalization group improvement in the theory of the Standard Model Higgs boson playing the role of an inflaton with a strong non-minimal coupling to gravity. It suggests the range of the Higgs mass 135.6 GeV≲MH≲184.5 GeV compatible with the current CMB data (the lower WMAP bound on ns), which is close to the widely accepted range dictated by the electroweak vacuum stability and perturbation theory bounds. We find the phenomenon of asymptotic freedom induced by this non-minimal curvature coupling, which brings the theory to the weak coupling domain everywhere except at the lower and upper boundary of this range. The renormalization group running of the basic quantityAI — the anomalous scaling in the non-minimally coupled Standard Model, which analytically determines all characteristics of the CMB spectrum — brings AI to small negative values at the inflation scale. This property is crucial for the above results and may also underlie the formation of initial conditions for the inflationary dynamics in quantum cosmology.
CMB cold spot
Effective field theory
False vacuum
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A bstract 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.
Yukawa potential
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A measurement of the Higgs boson mass is presented based on the combined data samples of the ATLAS and CMS experiments at the CERN LHC in the H→γγ and H→ZZ→4ℓ decay channels. The results are obtained from a simultaneous fit to the reconstructed invariant mass peaks in the two channels and for the two experiments. The measured masses from the individual channels and the two experiments are found to be consistent among themselves. The combined measured mass of the Higgs boson is mH=125.09±0.21 (stat)±0.11 (syst) GeV.Received 25 March 2015DOI:https://doi.org/10.1103/PhysRevLett.114.191803This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.© 2015 CERN, for the ATLAS and CMS Collab.
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The knowledge of the stability condition of the electroweak (EW) vacuum is of the greatest importance for our understanding of beyond Standard Model (BSM) physics. It is widely believed that new physics that lives at very high energy scales should have no impact on the stability analysis. This expectation has been recently challenged, but the results were controversial as new physics was given in terms of non-renormalizable higher order operators. Here we consider for the first time a renormalizable (toy) UV completion of the SM, and definitely show that such a decoupling does not take place. This result has important phenomenological consequences, providing a very useful test for BSM theories. In particular, it shows that speculations based on the so called “criticality” do not appear to be well founded.
Decoupling (probability)
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Spectral index
Planck mass
Effective field theory
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The stability of the standard model is determined by the true minimum of the effective Higgs potential. We show that the potential at its minimum when computed by the traditional method is strongly dependent on the gauge parameter. It moreover depends on the scale where the potential is calculated. We provide a consistent method for determining absolute stability independent of both gauge and calculation scale, order by order in perturbation theory. This leads to a revised stability bounds ${m}_{h}^{\text{pole}}>(129.4\ifmmode\pm\else\textpm\fi{}2.3)\text{ }\text{ }\mathrm{GeV}$ and ${m}_{t}^{\text{pole}}<(171.2\ifmmode\pm\else\textpm\fi{}0.3)\text{ }\text{ }\mathrm{GeV}$. We also show how to evaluate the effect of new physics on the stability bound without resorting to unphysical field values.
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False vacuum
Metastability
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