Standard Model Higgs Potential Research Articles

Higgs inflation via a metastable standard model potential, generalised renormalisation frame prescriptions and predictions for primordial gravitational waves

Higgs Inflation via a metastable Standard Model Higgs Potential is possible if the effective Planck mass in the Jordan frame increases after inflation ends. Here we consider the predictions of this model independently of the dynamics responsible for the Planck mass transition. The classical predictions are the same as for conventional Higgs Inflation. The quantum corrections are dependent upon the conformal frame in which the effective potential is calculated. We generalise beyond the usual Prescription I and II renormalisation frame choices to include intermediate frames characterised by a parameter α. We find that the model predicts a well-defined correlation between the values of the scalar spectral index ns and tensor-to-scalar ratio r. For values of ns varying between the 2-σ Planck observational limits, we find that r varies between 0.002 and 0.005 as ns increases, compared to the classical prediction of 0.003. Therefore significantly larger or smaller values of r are possible, which are correlated with larger or smaller values of ns . In addition, the model can be compatible with the larger values of ns predicted by Early Dark Energy solutions to the Hubble tension, with correspondingly larger values of r. The model can be tested via the detection of primordial gravitational waves by the next generation of CMB polarisation experiments.

Renormalisation of non-differentiable potentials

Non-differentiable potentials, such as the V-shaped (linear) potential, appear in various areas of physics. For example, the effective action for branons in the framework of the brane world scenario contains a Liouville-type interaction, i.e., an exponential of the V-shaped function. Another example is coming from particle physics when the standard model Higgs potential is replaced by a periodic self-interaction of an N-component scalar field which depends on the length, thus it is O(N) symmetric. We first compare classical and quantum dynamics near non-analytic points and discuss in this context the role of quantum fluctuations. We then study the renormalisation of such potentials, focusing on the Exact Wilsonian Renormalisation approach, and we discuss how quantum fluctuations smoothen the bare singularity of the potential. Applications of these results to the non-differentiable effective branon potential and to the O(N) models when the spatial dimension is varied and to the O(N) extension of the sine-Gordon model in (1+1) dimensions are presented.

Affine gravitational scenario for dark matter decay

Since the current evidence of its existence is revealed only through its gravitational influence, the way dark matter couples to gravity must be then of primary importance. Here, unlike the standard model sector which is typically coupled to metric, dark matter is supposed to couple only to spacetime affine connection through a $Z_2$-symmetry breaking term. We show that this structure leads to a coupling between dark matter, which is considered scalar, and the standard model Higgs potential. This induces dark matter decays into standard model particles through the Higgs which acts as a portal between the visible and the dark sectors. We study thoroughly the resulting decay modes for various mass ranges, and provide relevant bounds on the nonminimal coupling to affine gravity in line with observational data. Moreover, we find that the coupling to Higgs can be sufficiently large to facilitate production of dark matter lighter than 10 GeV at current and future high energy colliders.

Vacuum decay in the Standard Model: analytical results with running and gravity

A tunneling bounce driving the decay of a metastable vacuum must respect an integral constraint dictated by simple scaling arguments that is very useful to determine key properties of the bounce. After illustrating how this works in a simple toy model, the Standard Model Higgs potential is considered, including quartic coupling running and gravitational corrections as sources of scale invariance breaking. This approach clarifies the existence of the bounce and leads to simple and accurate analytical results in an expansion in the breaking parameters. Using the so-called tunneling-potential approach (generalized for nonminimal coupling to gravity) the integral constraint and the tunneling action are extended to second order in perturbations.

Inflation, proton decay, and Higgs-portal dark matter in SO(10) times U(1)_psi

We propose a simple non-supersymmetric grand unified theory (GUT) based on the gauge group SO(10) times U(1)_psi . The model includes 3 generations of fermions in mathbf{16} (+1), mathbf{10} (-2) and mathbf{1} (+4) representations. The mathbf{16}-plets contain Standard Model (SM) fermions plus right-handed neutrinos, and the mathbf{10}-plet and the singlet fermions are introduced to make the model anomaly-free. Gauge coupling unification at M_{GUT} simeq 5 times 10^{15}{-}10^{16} GeV is achieved by including an intermediate Pati–Salam breaking at M_{I} simeq 10^{12}{-}10^{11} GeV, which is a natural scale for the seesaw mechanism. For M_{I} simeq 10^{12}{-}10^{11}, proton decay will be tested by the Hyper-Kamiokande experiment. The extra fermions acquire their masses from U(1)_psi symmetry breaking, and a U(1)_psi Higgs field drives a successful inflection-point inflation with a low Hubble parameter during inflation, H_{inf} ll M_{I}. Hence, cosmologically dangerous monopoles produced from SO(10) and PS breakings are diluted away. This is the first SO(10) model we are aware of in which relatively light intermediate mass (sim 10^{10}{-}10^{12} GeV) primordial monopoles can be adequately suppressed. The reheating temperature after inflation can be high enough for successful leptogenesis. With the Higgs field contents of our model, a mathbf{Z}_2 symmetry remains unbroken after GUT symmetry breaking, and the lightest mass eigenstate among linear combinations of the mathbf{10}-plet and the singlet fermions serves as a Higgs-portal dark matter (DM). We identify the parameter regions to reproduce the observed DM relic density while satisfying the current constraint from the direct DM detection experiments. The present allowed region will be fully covered by the future direct detection experiments such as LUX-ZEPLIN DM experiment. In the presence of the extra fermions, the SM Higgs potential is stabilized up to M_{I}.

Higgs stability-bound and fermionic dark matter

Higgs-portal interactions of fermionic dark matter — in contrast to fermions coupled via Yukawa interactions — can have a stabilizing effect on the standard-model Higgs potential. A non-perturbative renormalization-group analysis reveals that, similar to higher-order operators in the Higgs potential itself, the fermionic portal coupling can increase the metastability scale by only about one order of magnitude. Assuming a thermal freeze-out via the Higgs-portal coupling, this regime of very weakly coupled dark matter is in conflict with relic-density constraints. Conversely, fermionic dark matter with the right relic abundance requires either a low cutoff scale of the effective field theory or a strongly interacting scalar sector. This results in a triviality problem in the scalar sector which persists at the non-perturbative level. The corresponding breakdown of the effective field theory suggests a larger dark sector to be present not too far above the dark-fermion mass-scale.

Higgs-portal assisted Higgs inflation with a sizeable tensor-to-scalar ratio

We show that the Higgs portal interactions involving extra dark Higgs field can save generically the original Higgs inflation of the standard model (SM) from the problem of a deep non-SM vacuum in the SM Higgs potential. Specifically, we show that such interactions disconnect the top quark pole mass from inflationary observables and allow multi-dimensional parameter space to save the Higgs inflation, thanks to the additional parameters (the dark Higgs boson mass mϕ, the mixing angle α between the SM Higgs H and dark Higgs Φ, and the mixed quartic coupling) affecting RG-running of the Higgs quartic coupling. The effect of Higgs portal interactions may lead to a larger tensor-to-scalar ratio, 0.08 ≲ r ≲ 0.1, by adjusting relevant parameters in wide ranges of α and mϕ, some region of which can be probed at future colliders. Performing a numerical analysis we find an allowed region of parameters, matching the latest Planck data.

Sphalerons in composite and nonstandard Higgs models

After the discovery of the Higgs boson and the rather precise measurement of all electroweak boson's masses the local structure of the electroweak symmetry breaking potential is already quite well established. However, despite being a key ingredient to a fundamental understanding of the underlying mechanism of electroweak symmetry breaking, the global structure of the electroweak potential remains entirely unknown. The existence of sphalerons, unstable solutions of the classical action of motion that are interpolating between topologically distinct vacua, is a direct consequence of the Standard Model's $\mathrm{SU}(2)_L$ gauge group. Nevertheless, the sphaleron energy depends on the shape of the Higgs potential away from the minimum and can therefore be a litmus test for its global structure. Focusing on two scenarios, the minimal composite Higgs model $\mathrm{SO}(5)/\mathrm{SO}(4)$ or an elementary Higgs with a deformed electroweak potential, we calculate the change of the sphaleron energy compared to the Standard Model prediction. We find that the sphaleron energy would have to be measured to $\mathcal{O}(10)\%$ accuracy to exclude sizeable global deviations from the Standard Model Higgs potential. We further find that because of the periodicity of the scalar potential in composite Higgs models a second sphaleron branch with larger energy arises.

Stationary configurations of the Standard Model Higgs potential: Electroweak stability and rising inflection point

We study the gauge-independent observables associated with two interesting stationary configurations of the Standard Model Higgs potential (extrapolated to high energy according to the present state of the art, namely the NNLO): i) the value of the top mass ensuring stability of the SM electroweak minimum, and ii) the value of the Higgs potential at a rising inflection point. We examine in detail and reappraise the experimental and theoretical uncertainties which plague their determination, finding that: i) stability of the SM is compatible with the present data at the 1.5 sigma level; ii) despite the large theoretical error plaguing the value of the Higgs potential at a rising inflection point, application of such configuration to models of primordial inflation displays a 3 sigma tension with the recent bounds on the tensor-to-scalar ratio of cosmological perturbations.

Solving the wrong hierarchy problem

Many theories require augmenting the Standard Model with additional scalar fields with large order one couplings. We present a new solution to the hierarchy problem for these scalar fields. We explore parity- and $\mathbb{Z}_2$-symmetric theories where the Standard Model Higgs potential has two vacua. The parity or $\mathbb{Z}_2$ copy of the Higgs lives in the minimum far from the origin while our Higgs occupies the minimum near the origin of the potential. This approach results in a theory with multiple light scalar fields but with only a single hierarchy problem, since the bare mass is tied to the Higgs mass by a discrete symmetry. The new scalar does not have a new hierarchy problem associated with it because its expectation value and mass are generated by dimensional transmutation of the scalar quartic coupling. The location of the second Higgs minimum is not a free parameter, but is rather a function of the matter content of the theory. As a result, these theories are extremely predictive. We develop this idea in the context of a solution to the strong CP problem. We show this mechanism postdicts the top Yukawa to be within $1 \sigma$ of the currently measured value and predicts scalar color octets with masses in the range 9-200 TeV.

Is a Higgs vacuum instability fatal for high-scale inflation?

We study the inflationary evolution of a scalar field $h$ with an unstable potential for the case where the Hubble parameter $H$ during inflation is larger than the instability scale ${\mathrm{\ensuremath{\Lambda}}}_{I}$ of the potential. Quantum fluctuations in the field of size $\ensuremath{\delta}h\ensuremath{\sim}\frac{H}{2\ensuremath{\pi}}$ imply that the unstable part of the potential is sampled during inflation. We investigate the evolution of these fluctuations to the unstable regime and in particular whether they generate cosmological defects or even terminate inflation. We apply the results of a toy scalar model to the case of the Standard Model Higgs boson, the quartic of which evolves to negative values at high scales, and extend previous analyses of Higgs dynamics during inflation utilizing statistical methods to a perturbative and fully gauge-invariant formulation. We show that the dynamics are controlled by the renormalization group-improved quartic coupling $\ensuremath{\lambda}(\ensuremath{\mu})$ evaluated at a scale $\ensuremath{\mu}=H$, such that Higgs fluctuations are enhanced by the instability if $H>{\mathrm{\ensuremath{\Lambda}}}_{I}$. Even if $H>{\mathrm{\ensuremath{\Lambda}}}_{I}$, the instability in the Standard Model Higgs potential does not end inflation; instead the universe slowly sloughs off crunching patches of space that never come to dominate the evolution. As inflation proceeds past 50 $e$-folds, a significant proportion of patches exits inflation in the unstable vacuum, and as much as 1% of the spacetime can rapidly evolve to a defect. Depending on the nature of these defects, however, the resulting universe could still be compatible with ours.

Electroweak Vacuum Stability in Light of BICEP2

We consider the effect of a period of inflation with a high energy density upon the stability of the Higgs potential in the early Universe. The recent measurement of a large tensor-to-scalar ratio, rT∼0.16, by the BICEP2 experiment possibly implies that the energy density during inflation was very high, comparable with the GUT scale. Given that the standard model Higgs potential is known to develop an instability at Λ∼1010 GeV this means that the resulting large quantum fluctuations of the Higgs field could destabilize the vacuum during inflation, even if the Higgs field starts at zero expectation value. We estimate the probability of such a catastrophic destabilization given such an inflationary scenario, and calculate that for a Higgs boson mass of mh=125.5 GeV that the top mass must be less than mt∼172 GeV. We present two possible cures: a direct coupling between the Higgs field and the inflaton and a nonzero temperature from dissipation during inflation.Received 16 April 2014DOI:https://doi.org/10.1103/PhysRevLett.112.201801© 2014 American Physical Society

Towards completing the standard model: Vacuum stability, electroweak symmetry breaking, and dark matter

We study the standard model (SM) in its full perturbative validity range between ${\mathrm{\ensuremath{\Lambda}}}_{\mathrm{QCD}}$ and the $U{(1)}_{Y}$ Landau pole, assuming that a yet unknown gravitational theory in the UV does not introduce additional particle thresholds, as suggested by the tiny cosmological constant and the absence of new stabilizing physics at the electroweak scale. We find that, due to dimensional transmutation, the SM Higgs potential has a global minimum at ${10}^{26}\text{ }\text{ }\mathrm{GeV}$, invalidating the SM as a phenomenologically acceptable model in this energy range. We show that extending the classically scale invariant SM with one complex singlet scalar $S$ allows us to (i) stabilize the SM Higgs potential, (ii) induce a scale in the singlet sector via dimensional transmutation that generates the negative SM Higgs mass term via the Higgs portal, (iii) provide a stable $CP$-odd singlet as the thermal relic dark matter due to $CP$-conservation of the scalar potential, and (iv) provide a degree of freedom that can act as an inflaton in the form of the $CP$-even singlet. The logarithmic behavior of dimensional transmutation allows one to accommodate the large hierarchy between the electroweak scale and the Landau pole, while understanding the latter requires a new nonperturbative view on the SM.

Higgs mass and vacuum stability in the Standard Model at NNLO

Abstract 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.

Dark energy from neutrinos and standard model Higgs potential

The dark energy density of the universe is obtained from the Higgs potential by introducing a Higgs-dependent neutrino mass. In the standard picture of electro-weak symmetry breaking the Higgs potential is Vϕ=(λ/4)(ϕ2−v2)2 and the Higgs field rolls down to the minima at 〈ϕ〉=v=246.2GeV and the net vacuum energy is zero. Now if the neutrino mass is a function of the Higgs field, then the vacuum expectation value of the Higgs is determined by maximizing the total pressure of the Higgs self interaction and the neutrino fluid Pϕ+Pν(m(ϕ)) w.r.t ϕ. The new minima 〈ϕ〉=v+σm shifts from the standard Higgs vev v by a small amount σm. The total pressure of the Higgs-neutrino coupled fluid Pϕ(v+σm)+Pν(v+σm)=−ρΛ appears as the dark energy density of the universe. The magnitude of the dark energy is thus determined by to the neutrino mass and the Higgs potential.