Effective Higgs Potential Research Articles

Weak-scale Higgs inflation

The present measurement of the Standard Model (SM) parameters suggests that the Higgs effective potential has a maximum at the Higgs field value of approximately 1011GeV, and the electroweak (EW) vacuum is not absolutely stable. To achieve absolute EW stability, a very large Higgs-Ricci scalar non-minimal coupling can be introduced.I study cosmic inflation driven by the Higgs field in this extension of the SM and refer to it as “weak-scale Higgs inflation” because the resulting inflationary Hubble parameter is around the weak scale. The Palatini formulation of gravity with a dimension 6 term is shown to drive successful inflation. I also argue for the UV (in)sensitivity of the predictions, and phenomenological implications. In the metric formulation case, the scenario for stable EW vacuum may be probed by measuring the Higgs coupling in future colliders.

Neutrinos, dark matter and Higgs vacua in parity solutions of the strong CP problem

The strong CP problem can be solved if the laws of nature are invariant under a space-time parity exchanging the Standard Model with its mirror copy. We review and extend different realizations of this idea with the aim of discussing Dark Matter, neutrino physics, leptogenesis and collider physics within the same context. In the minimal realization of ref. [1] the mirror world contains a massless dark photon, which leads to a rather interesting cosmology. Mirror electrons reproduce the dark matter abundance for masses between 500–1000 GeV with traces of strongly interacting dark matter. This scenario also predicts deviations from cold dark matter, sizable ∆Neff and colored states in the TeV range that will be tested in a variety of upcoming experiments. We also explore scenarios where the mirror photon is massive and the mirror particles are charged under ordinary electromagnetism with very different phenomenology. We also show that, for the measured values of the SM parameters, the Higgs effective potential can give rise to a second minimum at large field value as required to break spontaneously the parity symmetry.

A strongly first-order electroweak phase transition from Loryons

We study the effect of BSM particles receiving most of their mass from their coupling to the Higgs boson (“Loryons”) on the electroweak phase transition. The existence of BSM Loryons would imply that electroweak symmetry must be non-linearly realized in the effective theory of the Standard Model. Since, by definition, Loryons have a significant coupling to the Higgs, they are expected to have a significant effect on the Higgs effective potential and thereby the electroweak phase transition. We show that the BSM Loryon parameter space viable under current experimental and theoretical constraints overlaps heavily with the parameter space in which a strongly first-order phase transition is predicted. The portion of the experimentally allowed parameter space which gives a strongly first-order phase transition is significantly larger for Loryons as compared to non-Loryons.

The UV sensitivity of the Higgs potential in Gauge–Higgs Unification

Abstract In this paper, we discuss the UV sensitivity of the Higgs effective potential in a Gauge--Higgs Unification (GHU) model. We consider an $SU(\mathcal N)$ GHU on $\mathbf M^4\times S^1$ spacetime with a massless Dirac fermion. In this model, we evaluate the four-Fermi diagrams at the two-loop level and find them to be logarithmically divergent in the dimensional regularization scheme. Moreover, we confirm that their counter-terms contribute to the Higgs effective potential at the four-loop level. This result means that the Higgs effective potential in the GHU depends on UV theories as well as in other non-renormalizable theories.

Vacuum decay constraints on the Higgs curvature coupling from inflation

We derive lower bounds for the Higgs-curvature coupling from vacuum stability during inflation in three inflationary models: quadratic and quartic chaotic inflation, and Starobinsky-like power-law inflation. In contrast to most previous studies we take the time-dependence of the Hubble rate into account both in the geometry of our past light-cone and in the Higgs effective potential, which is approximated with three-loop renormalisation group improvement supplemented with one-loop curvature corrections. We find that in all three models, the lower bound is ξ≳ 0.051… 0.066 depending on the top quark mass. We also demonstrate that vacuum decay is most likely to happen a few e-foldings before the end of inflation.

To be, or not to be finite? The Higgs potential in Gauge-Higgs Unification

In this paper, we investigate the finiteness of the Higgs effective potential in an SU( mathcal{N} ) Gauge-Higgs Unification (GHU) model defined on M4× S1. We obtain the Higgs effective potential at the two-loop level and find that it is finite. We also discuss that the Higgs effective potential is generically divergent for three- or higher-loop levels. As an example, we consider an SU( mathcal{N} ) gauge theory on M5× S1, where the one-loop corrections to the four-Fermi operators are divergent. We find that the Higgs effective potential depends on their counter terms at the three-loop level.

Constrained hybrid Monte Carlo algorithms for gauge–Higgs models

We develop Hybrid Monte Carlo (HMC) algorithms for constrained Hamiltonian systems of gauge–Higgs models and introduce a new observable for the constraint effective Higgs potential. We use an extension of the so-called Rattle algorithm to general Hamiltonians for constrained systems, which we adapt to the 4D Abelian–Higgs model and the 5D SU(2) gauge theory on the torus and on the orbifold. The derivative of the potential is measured via the expectation value of the Lagrange multiplier for the constraint condition and allows a much more precise determination of the effective potential than conventional histogram methods. With the new method, we can access the potential over the full domain of the Higgs variable, while the histogram method is restricted to a short region around the expectation value of the Higgs field in unconstrained simulations, and the statistical precision does not deteriorate when the volume is increased. We further verify our results by comparing to the one-loop Higgs potential of the 4D Abelian–Higgs model in unitary gauge and find good agreement. To our knowledge, this is the first time this problem has been addressed for theories with gauge fields. The algorithm can also be used in four dimensions to study finite temperature and density transitions via effective Polyakov loop actions.

Top-down Approach to the Curved Spacetime Effective Field Theory (cEFT) — Theory and Examples

The effective field theory (EFT) turns out to be an instrument of an immense value in all aspects of modern particle physics being theory, phenomenology or experiment. In the paper I will show how to extend the systematic top down approach to construction of the EFT proposed by Hitoshi Murayama (LBL, Berkeley) and separately by John Ellis (King's Coll. London) groups to the curved spacetime. To this end, I will take advantage of the heat kernel method so far extensively used in obtaining the one-loop effective action in curved spacetime. After an introduction of the formalism I will discuss its application to the problem of an influence of gravity on the stability of the Higgs effective potential.

Cosmological Constant in SUGRA Models with Degenerate Vacua

The extrapolation of couplings up to the Planck scale within the standard model (SM) indicates that the Higgs effective potential can have two almost degenerate vacua, which were predicted by the multiple point principle (MPP). The application of the MPP to ( N = 1 ) supergravity (SUGRA) implies that the SUGRA scalar potential of the hidden sector possesses at least two exactly degenerate minima. The first minimum is associated with the physical phase in which we live. In the second supersymmetric (SUSY) Minkowski vacuum, the local SUSY may be broken dynamically, inducing a tiny vacuum energy density. In this paper, we consider the no-scale-inspired SUGRA model in which the MPP conditions are fulfilled without any extra fine-tuning at the tree-level. Assuming that at high energies, the couplings in both phases are identical, one can estimate the dark energy density in these vacua. Using the two-loop renormalization group (RG) equations, we find that the measured value of the cosmological constant can be reproduced if the SUSY breaking scale M S in the physical phase is of the order of 100 TeV. The scenario with the Planck scale SUSY breaking is also discussed.

Higgs vacuum stability with vectorlike fermions

We present the effects of vector-like fermions (VLF) on the stability of the Higgs electroweak vacuum, using the renormalization group improved Higgs effective potential. We review the calculation of the one-loop beta-functions of the standard model couplings, paying particular attention to the fermion contributions. From this, we derive the VLF contributions to the beta-functions. We also include the significant two-loop contributions to the beta-functions. Using these beta-functions we determine the scale at which the effective Higgs quartic-coupling becomes zero and goes negative, signaling vacuum instability. We find that for certain VLF masses and Yukawa couplings, the Higgs quartic stays positive for field values all the way up to the Planck scale, implying that the meta-stable vacuum of the standard model can be rendered absolutely stable if VLFs are present with certain parameters. For other values of VLF parameters, the Higgs vacuum is metastable as in the standard model. For cases where the vacuum is metastable, we compute the probability of quantum tunneling from the false electroweak vacuum into a deeper true vacuum in our Hubble volume by numerically solving for the bounce configuration in Euclidean space-time and computing the bounce action for it. We compare our numerical solution with the analytical approximation for the bounce action commonly used in the literature and comment on when the latter may be used.

Direct Higgs-gravity interaction and stability of our universe

The Higgs effective potential becomes unstable at approximately $10^{11}$ GeV, and if only standard model interactions are considered, the lifetime $\tau$ of the electroweak vacuum turns out to be much larger than the age of the Universe $T_U$. It is well known, however, that $\tau$ is extremely sensitive to the presence of unknown new physics: the latter can enormously lower $\tau$. This poses a serious problem for the stability of our Universe, demanding for a physical mechanism that protects it from a disastrous decay. We have found that there exists a universal stabilizing mechanism that naturally originates from the nonminimal coupling between gravity and the Higgs boson. As this Higgs-gravity interaction necessarily arises from the quantum dynamics of the Higgs field in a gravitational background, this stabilizing mechanism is certainly present. It is not related to any specific model, being rather natural and universal as it comes from fundamental pillars of our physical world: gravity, the Higgs field, the quantum nature of physical laws.

Nonpolynomial Higgs interactions and vacuum stability

The possible violation of the conventional lower Higgs mass stability bound by the discovered Higgs boson has far reaching consequences within particle physics and cosmology. We discuss the possibility that nonpolynomial bare interactions seeded at some high-momentum scale can considerably diminish the lower Higgs mass bound without introducing a metastability in the Higgs effective potential. For this, we classify various deformations of the usual quartic bare potential regarding their impact on stable IR physics. We perform the analysis in a large N_{mathrm {f}} expansion, addressing the convergence of the obtained results by taking 1/N_{mathrm {f}} corrections into account as well. In addition, we investigate the renormalization group flow of the scalar potential on a nonperturbative level. Within these approximations, we are able to identify bare potentials that lead to Higgs masses below stability mass bounds obtained from finite-order polynomial bare interactions without introducing a metastability in the effective potential.

Ruling out critical Higgs inflation?

We consider critical Higgs inflation, namely Higgs inflation with a rising inflection point at smaller field values than those of the plateau induced by the non-minimal coupling to gravity. It has been proposed that such configuration is compatible with the present CMB observational constraints on inflation, and also with primordial black hole production accounting for the totality or a fraction of the observed dark matter. We study the model taking into account the NNLO corrections to the Higgs effective potential: such corrections are extremely important to reduce the theoretical error associated to the calculation. We find that, in the 3 sigma window for the relevant low energy parameters, which are the strong coupling and the Higgs mass (the top mass follows by requiring an inflection point), the potential at the inflection point is so large (and so is the Hubble constant during inflation) that the present bound on the tensor-to-scalar ratio is violated. The model is viable only allowing the strong coupling to take its upper 3-4 sigma value. In our opinion, this tension shows that the model of critical Higgs inflation is likely to be not viable: neither inflation nor black holes as dark matter can be originated in this version of the model.

Impact of generalized Yukawa interactions on the lower Higgs-mass bound

We investigate the impact of operators of higher canonical dimension on the lower Higgs-mass consistency bound by means of generalized Higgs–Yukawa interactions. Analogously to higher-order operators in the bare Higgs potential in an effective field theory approach, the inclusion of higher-order Yukawa interactions, e.g., phi ^3bar{psi }psi , leads to a diminishing of the lower Higgs-mass bound and thus to a shift of the scale of new physics towards larger scales by a few orders of magnitude without introducing a metastability in the effective Higgs potential. We observe that similar renormalization group mechanisms near the weak-coupling fixed point are at work in both generalizations of the microscopic action. Thus, a combination of higher-dimensional operators with generalized Higgs as well as Yukawa interactions does not lead to an additive shift of the lower mass bound, but it relaxes the consistency bounds found recently only slightly. On the method side, we clarify the convergence properties of different projection and expansion schemes for the Yukawa potential used in the functional renormalization group literature so far.

Meaning of the field dependence of the renormalization scale in Higgs inflation

We consider the prescription dependence of the Higgs effective potential under the presence of general nonminimal couplings. We evaluate the fermion loop correction to the effective action in a simplified Higgs-Yukawa model whose path integral measure takes simple form either in the Jordan or Einstein frame. The resultant effective action becomes identical in both cases when we properly take into account the quartically divergent term coming from the change of measure. Working in the counterterm formalism, we clarify that the difference between the prescriptions I and II comes from the counter term to cancel the logarithmic divergence. This difference can be absorbed into the choice of tree-level potential from the infinitely many possibilities, including all the higher-dimensional terms. We also present another mechanism to obtain a flat potential by freezing the running of the effective quartic coupling for large field values, using the nonminimal coupling in the gauge kinetic function.

Erratum: Higgs effective potential in a perturbed Robertson-Walker background [Phys. Rev. D90, 123541 (2014)

Erratum: Higgs effective potential in a perturbed Robertson-Walker background [Phys. Rev. D<b>90</b>, 123541 (2014)

Stability of the Electroweak Vacuum: Gauge Independence and Advanced Precision.

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.

Stability of the effective potential of the gauge-less top-Higgs model in curved spacetime

We investigate stability of the Higgs effective potential in curved spacetime. To this end, we consider the gauge-less top-Higgs sector with an additional scalar field. Explicit form of the terms proportional to the squares of the Ricci scalar, the Ricci tensor and the Riemann tensor that arise at the one-loop level in the effective action has been determined. We have investigated the influence of these terms on the stability of the scalar effective potential. The result depends on background geometry. In general, the potential becomes modified both in the region of the electroweak minimum and in the region of large field strength.

Higgs inflation, seesaw physics and fermion dark matter

We present an inflationary model in which the Standard Model Higgs doublet field with non-minimal coupling to gravity drives inflation, and the effective Higgs potential is stabilized by new physics which includes a dark matter particle and right-handed neutrinos for the seesaw mechanism. All of the new particles are fermions, so that the Higgs doublet is the unique inflaton candidate. With central values for the masses of the top quark and the Higgs boson, the renormalization group improved Higgs potential is employed to yield the scalar spectral index ns≃0.968, the tensor-to-scalar ratio r≃0.003, and the running of the spectral index α=dns/dln⁡k≃−5.2×10−4 for the number of e-folds N0=60 (ns≃0.962, r≃0.004, and α≃−7.5×10−4 for N0=50). The fairly low value of r≃0.003 predicted in this class of models means that the ongoing space and land based experiments are not expected to observe gravity waves generated during inflation.

A scale-invariant Higgs sector and structure of the vacuum

In view of the current status of measured Higgs boson properties, we consider a question whether only the Higgs self-interactions can deviate significantly from the Standard-Model (SM) predictions. This may be possible if the Higgs effective potential is irregular at the origin. As an example we investigate an extended Higgs sector with singlet scalar(s) and classical scale invariance. We develop a perturbative formulation necessary to analyze this model in detail. The behavior of a phenomenologically valid potential in the perturbative regime is studied around the electroweak scale. We reproduce known results: the Higgs self-interactions are substantially stronger than the SM predictions, while the Higgs interactions with other SM particles are barely changed. We further predict that the interactions of singlet scalar(s), which is a few to several times heavier than the Higgs boson, tend to be fairly strong. If probed, these features will provide vivid clues to the structure of the vacuum. We also examine Veltman’s condition for the Higgs boson mass.