Electroweak Vacuum Instability Research Articles

On the cosmological implications of the electroweak vacuum instability: constraining the non-minimal coupling with inflation

Our current measurements of the Standard Model parameters imply that the Higgs field resides in a metastable electroweak vacuum, where the vacuum can decay to a lower ground state, with cataclysmic repercussions for our Universe. According to our observations, no such event has happened in the observable universe, in spite of the various energetic processes that could have triggered it. This work serves as an overview of a method that uses the metastability of the false vacuum during cosmological inflation to provide constraints on the Higgs curvature coupling ξ. Considering also the effects of the time-dependent Hubble rate on the effective Higgs potential and on our past light-cone space-time geometry, results in state-of-the-art lower ξ-bounds from quadratic and quartic chaotic inflation, and Starobinsky-like power-law inflation.

Higgs cosmology.

The discovery of the Higgs boson in 2012 and other results from the Large Hadron Collider have confirmed the standard model of particle physics as the correct theory of elementary particles and their interactions up to energies of several TeV. Remarkably, the theory may even remain valid all the way to the Planck scale of quantum gravity, and therefore it provides a solid theoretical basis for describing the early Universe. Furthermore, the Higgs field itself has unique properties that may have allowed it to play a central role in the evolution of the Universe, from inflation to cosmological phase transitions and the origin of both baryonic and dark matter, and possibly to determine its ultimate fate through the electroweak vacuum instability. These connections between particle physics and cosmology have given rise to a new and growing field of Higgs cosmology, which promises to shed new light on some of the most puzzling questions about the Universe as new data from particle physics experiments and cosmological observations become available.This article is part of the Theo Murphy meeting issue 'Higgs cosmology'.

Do metric fluctuations affect the Higgs dynamics during inflation?

We show that the dynamics of the Higgs field during inflation is not affected by metric fluctuations if the Higgs is an energetically subdominant light spectator. For Standard Model parameters we find that couplings between Higgs and metric fluctuations are suppressed by \U0001d4aa(10−7). They are negligible compared to both pure Higgs terms in the effective potential and the unavoidable non-minimal Higgs coupling to background scalar curvature. The question of the electroweak vacuum instability during high energy scale inflation can therefore be studied consistently using the Jordan frame action in a Friedmann-Lemaître-Robertson-Walker metric, where the Higgs-curvature coupling enters as an effective mass contribution. Similar results apply for other light spectator scalar fields during inflation.

Electroweak vacuum instability and renormalized Higgs field vacuum fluctuations in the inflationary universe

In this work, we investigated the electroweak vacuum instability during or after inflation. In the inflationary Universe, i.e., de Sitter space, the vacuum field fluctuations < δ ϕ 2 > enlarge in proportion to the Hubble scale H2. Therefore, the large inflationary vacuum fluctuations of the Higgs field < δ ϕ 2 > are potentially catastrophic to trigger the vacuum transition to the negative-energy Planck-scale vacuum state and cause an immediate collapse of the Universe. However, the vacuum field fluctuations < δ ϕ 2 >, i.e., the vacuum expectation values have an ultraviolet divergence, and therefore a renormalization is necessary to estimate the physical effects of the vacuum transition. Thus, in this paper, we revisit the electroweak vacuum instability from the perspective of quantum field theory (QFT) in curved space-time, and discuss the dynamical behavior of the homogeneous Higgs field ϕ determined by the effective potential V eff( ϕ ) in curved space-time and the renormalized vacuum fluctuations < δ ϕ 2 >ren via adiabatic regularization and point-splitting regularization. We simply suppose that the Higgs field only couples the gravity via the non-minimal Higgs-gravity coupling ξ(μ). In this scenario, the electroweak vacuum stability is inevitably threatened by the dynamical behavior of the homogeneous Higgs field ϕ, or the formations of AdS domains or bubbles unless the Hubble scale is small enough H< ΛI .

Electroweak vacuum stability in classically conformal B-L extension of the standard model

We consider the minimal U(1)_{B-L} extension of the standard model (SM) with the classically conformal invariance, where an anomaly-free U(1)_{B-L} gauge symmetry is introduced along with three generations of right-handed neutrinos and a U(1)_{B-L} Higgs field. Because of the classically conformal symmetry, all dimensional parameters are forbidden. The B-L gauge symmetry is radiatively broken through the Coleman–Weinberg mechanism, generating the mass for the U(1)_{B-L} gauge boson (Z^prime boson) and the right-handed neutrinos. Through a small negative coupling between the SM Higgs doublet and the B-L Higgs field, the negative mass term for the SM Higgs doublet is generated and the electroweak symmetry is broken. In this model context, we investigate the electroweak vacuum instability problem in the SM. It is well known that in the classically conformal U(1)_{B-L} extension of the SM, the electroweak vacuum remains unstable in the renormalization group analysis at the one-loop level. In this paper, we extend the analysis to the two-loop level, and perform parameter scans. We identify a parameter region which not only solve the vacuum instability problem, but also satisfy the recent ATLAS and CMS bounds from search for Z^prime boson resonance at the LHC Run-2. Considering self-energy corrections to the SM Higgs doublet through the right-handed neutrinos and the Z^prime boson, we derive the naturalness bound on the model parameters to realize the electroweak scale without fine-tunings.

Classically conformalU(1)′extended standard model, electroweak vacuum stability, and LHC Run-2 bounds

We consider the minimal U(1)' extension of the standard model (SM) with the classically conformal invariance, where an anomaly-free U(1)' gauge symmetry is introduced along with three generations of right-handed neutrinos and a U(1)' Higgs field. Since the classically conformal symmetry forbids all dimensional parameters in the model, the U(1)' gauge symmetry is broken by the Coleman-Weinberg mechanism, generating the mass terms of the U(1)' gauge boson ($Z$' boson) and the right-handed neutrinos. Through a mixing quartic coupling between the U(1)' Higgs field and the SM Higgs doublet field, the radiative U(1)' gauge symmetry breaking also triggers the breaking of the electroweak symmetry. In this model context, we first investigate the electroweak vacuum instability problem in the SM. Employing the renormalization group equations at the two-loop level and the central values for the world average masses of the top quark ($m_t=173.34$ GeV) and the Higgs boson ($m_h=125.09$ GeV), we perform parameter scans to identify the parameter region for resolving the electroweak vacuum instability problem. Next we interpret the recent ATLAS and CMS search limits at the LHC Run-2 for the sequential $Z$' boson to constrain the parameter region in our model. Combining the constraints from the electroweak vacuum stability and the LHC Run-2 results, we find a bound on the $Z$' boson mass as $m_{Z'} \gtrsim 3.5$ TeV. We also calculate self-energy corrections to the SM Higgs doublet field through the heavy states, the right-handed neutrinos and the $Z$' boson, and find the naturalness bound as $m_{Z'} \lesssim 7$ TeV, in order to reproduce the right electroweak scale for the fine-tuning level better than 10\%. The resultant mass range of $3.5$ TeV $\lesssim m_{Z'} \lesssim 7$ TeV will be explored at the LHC Run-2 in the near future.

21pAL-9 Electroweak Vacuum Instability from Inflation to Preheating, Reheating Stage

21pAL-9 Electroweak Vacuum Instability from Inflation to Preheating, Reheating Stage

Probable or improbable universe? Correlating electroweak vacuum instability with the scale of inflation

Measurements of the Higgs boson and top quark masses indicate that the Standard Model Higgs potential becomes unstable around Λ I ∼ 1011 GeV. This instability is cosmologically relevant since quantum fluctuations during inflation can easily destabilize the electroweak vacuum if the Hubble parameter during inflation is larger than Λ I (as preferred by the recent BICEP2 measurement). We perform a careful study of the evolution of the Higgs field during inflation, obtaining different results from those currently in the literature. We consider both tunneling via a Coleman-de Luccia or Hawking-Moss instanton, valid when the scale of inflation is below the instability scale, as well as a statistical treatment via the Fokker-Planck equation appropriate in the opposite regime. We show that a better understanding of the post-inflation evolution of the unstable AdS vacuum regions is crucial for determining the eventual fate of the universe. If these AdS regions devour all of space, a universe like ours is indeed extremely unlikely without new physics to stabilize the Higgs potential; however, if these regions crunch, our universe survives, but inflation must last a few e-folds longer to compensate for the lost AdS regions. Lastly, we examine the effects of generic Planck-suppressed corrections to the Higgs potential, which can be sufficient to stabilize the electroweak vacuum during inflation.

Higgs vacuum stability and inflationary dynamics after BICEP2 and PLANCK dust polarisation data

If the recent detection of B-mode polarization of the Cosmic Microwave Background by BICEP2 observations, withstand the test of time after the release of recent PLANCK dust polarisation data, then it would surprisingly put the inflationary scale near Grand Unification scale if one considers single-field inflationary models. On the other hand, Large Hadron Collider has observed the elusive Higgs particle whose presently observed mass can lead to electroweak vacuum instability at high scale (∼ \U0001d4aa(1010) GeV). In this article, we seek for a simple particle physics model which can simultaneously keep the vacuum of the theory stable and yield high-scale inflation successfully. To serve our purpose, we extend the Standard Model of particle physics with a U(1)B-L gauged symmetry which spontaneously breaks down just above the inflationary scale. Such a scenario provides a constrained parameter space where both the issues of vacuum stability and high-scale inflation can be successfully accommodated. The threshold effect on the Higgs quartic coupling due to the presence of the heavy inflaton field plays an important role in keeping the electroweak vacuum stable. Furthermore, this scenario is also capable of reheating the universe at the end of inflation. Though the issues of Dark Matter and Dark Energy, which dominate the late-time evolution of our universe, cannot be addressed within this framework, this model successfully describes the early universe dynamics according to the Big Bang model.

Stabilizing electroweak vacuum in a vectorlike fermion model

To avoid possible electroweak vacuum instability in the vectorlike fermion model, we introduce a new singlet scalar to the model, which couples to the vectorlike fermion and also mixes with the Higgs boson after spontaneous symmetry breaking. We investigate the vectorlike fermion predominantly coupled to the third-generation quarks, and its mass is generated from the vacuum expectation value of the new scalar field in the model. In this setup, as running towards high energies, the new scalar provides a positive contribution to the running of the Higgs quartic coupling, and the matching on the scale of the scalar mass gives rise to a threshold effect that lifts up the Higgs quartic coupling strength. The two effects help stabilize the electroweak vacuum of the Higgs potential. Therefore, this setup could evade possible vacuum instability in the vectorlike fermion model. We show that a large range of parameter space is allowed to have both stable Higgs vacuum and perturbativity of all the running couplings, up to the Planck scale. We also examine the experimental constraints from the electroweak precision observables such as oblique corrections $S,T$ and nonoblique corrections to the $Z{b}_{L}{\overline{b}}_{L}$ coupling, the Higgs coupling precision measurements, and the current LHC direct searches.