Higgs Mass Parameter Research Articles

Spontaneous symmetry breaking, gauge hierarchy, and electroweak vacuum metastability

The so-called metastability bound asserts that an unnaturally small Higgs mass is a necessary condition for electroweak vacuum metastability, offering a new approach toward solving the hierarchy problem. So far, this result relies on the assumption of a negative Higgs mass parameter, or equivalently, on electroweak spontaneous symmetry breaking. We derive a new, corresponding bound for the case of a positive mass parameter. When the new bound is significantly more restrictive than or comparable to its established counterpart, it may offer an explanation for the sign of the Higgs mass parameter, and thus, spontaneous symmetry breaking itself. New physics at scales O(1–10) TeV can lower these bounds as far as the TeV scale. As an illustration, we consider vacuum stability in the presence of additional TeV-scale fermions with Yukawa couplings to the Higgs, as well as a dimension-six term parametrizing new physics in the UV. This scenario requires new physics that couples strongly to the Higgs, and can potentially be probed at future colliders. Finally, to allow for comparison with concrete mechanisms predicting metastability, we provide the mass-dependent lifetime of the electroweak vacuum for this model. Published by the American Physical Society 2024

Bringing the Peccei-Quinn mechanism down to Earth

It is conventionally assumed that the physics underlying the Peccei-Quinn (PQ) mechanism for addressing the strong CP problem is at very high energies, orders of magnitude above the weak scale. However, this may not be the case in general and the associated PQ boson ϕ, besides the signature state, i.e., the ultralight axion a, may emerge well below the weak scale. We consider this possibility and examine some of the conditions for its viability. The example model proposed here may also provide the requisite Standard Model Higgs mass parameter, without invoking new scalars above the giga-electron-volt (GeV) scale. The corresponding parameter space can maintain against quantum corrections. This scenario, depending on the choice of parameters, can potentially be constrained by flavor data. We point out that the current mild excess in B+→K+νν¯, reported by the Belle II experiment, could in principle be explained in this setup as B+→K+ϕ and B+→K+a, with both ϕ and a escaping the detector as missing energy. For a sufficiently heavy PQ boson, in the GeV regime (as the preferred explanation of the Belle II excess), one can separate these two contributions, due to the difference in K+ momenta. In this case, the axion may also affect lighter meson, e.g., kaon, decays while ϕ would not be a kinematically allowed final state. Published by the American Physical Society 2024

Tensor renormalization group study of (1 + 1)-dimensional U(1) gauge-Higgs model at θ = π with Lüscher’s admissibility condition

We investigate the phase structure of the (1+1)-dimensional U(1) gauge-Higgs model with a θ term, where the U(1) gauge action is constructed with Lüscher’s admissibility condition. Using the tensor renormalization group, both the complex action problem and topological freezing problem in the standard Monte Carlo simulation are avoided. We find the first-order phase transition with sufficiently large Higgs mass at θ = π, where the ℤ2 charge conjugation symmetry is spontaneously broken. On the other hand, the symmetry is restored with a sufficiently small mass. We determine the critical endpoint as a function of the Higgs mass parameter and show the critical behavior is in the two-dimensional Ising universality class.

Baryogenesis and dark matter in multiple hidden sectors

We explore a mechanism for producing the baryon asymmetry and dark matter in models with multiple hidden sectors that are Standard-Model-like but with varying Higgs mass parameters. If the field responsible for reheating the Standard Model and the exotic sectors carries an asymmetry, it can be converted into a baryon asymmetry using the standard sphaleron process. A hidden sector with positive Higgs mass squared can accommodate dark matter with its baryon asymmetry, and the larger abundance of dark matter relative to baryons is due to dark sphalerons being active all the way down the hidden sector QCD scale. This scenario predicts that dark matter is clustered in large dark nuclei and gives a lower bound on the effective relativistic degrees of freedom, ΔNeff≳0.05, which may be observable in the next-generation cosmic microwave background experiment CMB-S4. Published by the American Physical Society 2024

Gravitational Waves from Nnaturalness

We study the prospects for probing the Nnaturalness solution to the electroweak hierarchy problem with future gravitational wave observatories. Nnaturalness, in its simplest incarnation, predicts N copies of the Standard Model with varying Higgs mass parameters. We show that in certain parameter regions the scalar reheaton transfers a substantial energy density to the sector with the smallest positive Higgs squared mass while remaining consistent with bounds on additional effective relativistic species. In this sector, all six quarks are much lighter than the corresponding QCD confinement scale, allowing for the possibility of a first-order chiral symmetry-breaking phase transition and an associated stochastic gravitational wave signal. We consider several scenarios characterizing the strongly-coupled phase transition dynamics and estimate the gravitational wave spectrum for each. Pulsar timing arrays (SKA), spaced-based interferometers (BBO, Ultimate-DECIGO, μAres, asteroid ranging), and astrometric measurements (THEIA) all have the potential to explore new regions of Nnaturalness parameter space, complementing probes from next generation cosmic microwave background radiation experiments.

Electroweak phase transition with radiative symmetry breaking in a type-II seesaw model with an inert doublet

We consider the type-II seesaw model extended with another Higgs doublet, which is odd under the Z2 symmetry. We look for the possibility of triggering the electroweak symmetry breaking via radiative effects. The Higgs mass parameter changes sign from being positive at higher-energy scales to negative at lower-energy scales in the presence of the TeV scalar triplet. The Planck scale perturbativity is demanded and the electroweak phase transition is studied using two-loop β-functions. The maximum allowed values for the interaction quartic coupling of the second doublet field and the triplet field with the Higgs field are λ3=0.15 and λΦ1Δ=0.50, respectively. Considering these EW values, the first-order phase transition, i.e., ϕ+(Tc)/Tc∼0.6 is satisfied only for vanishing doublet and triplet bare mass parameters, mΦ2=0.0 GeV and mΔ=0.0 GeV. The small nonzero induced vacuum expectation value for the scalar triplet also generates the neutrino mass, and the lightest stable neutral particle from the inert doublet satisfies the dark matter constraints for the chosen parameter space. The impact of the thermal corrections on the stability of the electroweak vacuum is also studied, and the current experimental values of the Higgs mass and the top mass lie in the stable region both at the zero temperature and the finite temperature. Published by the American Physical Society 2024

Weak scale as a trigger

Does the value of the Higgs mass parameter affect the expectation value of local operators in the Standard Model? For essentially all local operators the answer to this question is "no", and this is one of the avatars of the hierarchy problem: nothing is "triggered" when the Higgs mass parameter crosses zero. In this letter, we explore settings in which Higgs mass parameters $can$ act as a "trigger" for some local operators ${\cal O}_T$. In the Standard Model, this happens for ${\cal O}_T = {\rm Tr} (G \tilde G)$. We also introduce a "type-0" two Higgs doublet model, with a $Z_4$ symmetry, for which ${\cal O}_T = H_1 H_2$ is triggered by the Higgs masses, demanding the existence of new Higgs states necessarily comparable to or lighter than the weak scale, with no wiggle room to decouple them whatsoever. Surprisingly, this model is not yet entirely excluded by collider searches, and will be incisively probed by the high-luminosity run of the LHC, as well as future Higgs factories. We also discuss a possibility for using this trigger to explain the origin of the weak scale, invoking a landscape of extremely light, weakly interacting scalars $\phi_i$, with a coupling to ${\cal O}_T$ needed to make it possible to find vacua with small enough cosmological constant. The weak scale trigger links the tuning of the Higgs mass to that of the cosmological constant, while coherent oscillations of the $\phi_i$ can constitute dark matter.

The Clockwork Standard Model

We consider various bulk fields with general dilaton couplings in the linear dilaton background in five dimensions as the continuum limit of clockwork models. We show that the localization of the zero modes of bulk fields and the mass gap in the KK spectrum depend not only on the bulk dilaton coupling, but also on the bulk mass parameter in the case of a bulk fermion. The consistency from universality and perturbativity of gauge couplings constrain the dilaton couplings to the brane-localized matter fields as well as the bulk gauge bosons. Constructing the Clockwork Standard Model (SM) in the linear dilaton background, we provide the necessary conditions for the bulk mass parameters for explaining the mass hierarchy and mixing for the SM fermions. We can introduce a sizable expansion parameter ε = {e}^{-frac{2}{3}{kz}_c} for the realistic flavor structure in the quark sector without a fine-tuning in the bulk mass parameters, but at the expense of a large 5D Planck scale. On the other hand, we can use a smaller expansion parameter for lepton masses, in favor of the solution to the hierarchy problem of the Higgs mass parameter. We found that massive Kaluza-Klein (KK) gauge bosons and massive KK gravitons couple more strongly to light and heavy fermions, respectively, so there is a complementarity in the resonance researches for those KK modes at the LHC.

Dark energy from Higgs potential

We derive the ratio of dark energy to baryon matter content in the universe from a Higgs potential matching a description of baryon matter on an intrinsic configuration space. The match determines the Higgs mass and self-coupling parameters and introduces a constant term in the Higgs potential. The constant term is taken to give dark energy contributions from detained neutrons, both primordial and piled-up neutrons from nuclear processes in stars. This corresponds to the dark energy content increasing with time. The two contributions possibly give rise to the primordial inflation and the later accelerated recession, respectively. The ensuing inflation during nucleosynthesis may explain the primordial lithium-seven deficit relative to the standard Big Bang nucleosynthesis model predictions. From the observed helium and stellar metallicity contents, we get a dark energy to baryon matter ratio of 14.5(0.7) to compare with the observed value of 13.9(0.2).

SUSY threshold corrections to quark and lepton mixing inspired by SO (10) GUT models

In the standard model (SM), the Cabibbo-Kobayashi-Maskawa (CKM) matrix is the only origin of flavor violations (FVs). On the other hand, in general, there are a lot of sources of the FVs in a physics beyond the SM, through the diagonalizing matrices which make Yukawa matrices diagonal. Although most of the diagonalizing matrices are unknown ones, grand unified theories (GUTs) can fix these matrices. In particular, if we consider a GUT model based on the SO(10) group, these diagonalizing matrices are strongly related to each other because of the matter unification. However, this unification causes the problem on the realization of measured SM fermion masses and mixing angles. Up to now, many people showed that supersymmetric (SUSY) threshold corrections can solve this problem, especially unfavorable fermion mass relations. In this paper, we show that how these SUSY threshold corrections affect unknown diagonalizing matrices. Since these contributions are also related to the FVs induced by SUSY particles, we can estimate the maximal effect to the diagonalizing matrices. We found that the (1, 3) and (3, 1) elements of diagonalizing matrices for quarks can be as large as the corresponding mixing angle of the CKM matrix. Moreover, we found that the higher SUSY scale can predict the larger mixing angles, although strong cancellation between the Higgs mass parameters is needed to realize the electroweak symmetry breaking.

Relaxation of Higgs mass and cosmological constant with four-form fluxes and reheating

We consider the most general effective action for the four-form fluxes in the Standard Model coupled to gravity. The Higgs mass parameter can be relaxed to a correct value due to the four-form coupling to the Higgs field and it stops changing due to an extremely suppressed transition probability from the observed cosmological constant to AdS space. We first introduce a non-minimal four-form coupling to gravity and discuss the role of a new scalar field as the inflaton and the conditions for a successful reheating at the end of relaxation.

Sterile Higgs Boson

To address the “little hierarchy problem,” we introduce two extra scalar fields neutral under the standard model gauge symmetry on top of the standard model. One linear combination of them has an almost flat potential, and so it can dynamically compensate the large Higgs mass parameter, while its small negative mass parameter can play the role of the electroweak symmetry breaking source. Thus the smallness of its mass parameter is responsible for the relatively small Higgs vacuum expectation value compared to a cut-off energy scale of the standard model. This scenario should eventually be embedded e.g. in a supersymmetric model, where the small mass parameters of the neutral singlets can be explained by employing both the gravity- and gauge-mediated supersymmetry breaking mechanisms. Their mixing angles with the Higgs boson can be suppressed enough (∼ 10−2), avoiding the phenomenological constraints. The mass of the lighter scalar field is of order sub-electroweak scale (∼ 10 GeV), when the heavier one is above TeV scale (∼ 5 TeV).

Higgs Naturalness and Renormalized Parameters

A recently popular formulation of the Higgs naturalness principle prohibits delicate cancellations between running renormalized Higgs mass parameters and EFT matching corrections, by contrast with the principle’s original formulation, which prohibits delicate cancellations between the bare Higgs mass parameter and its quantum corrections. While the need for this latter cancellation is sometimes viewed as unproblematic since bare parameters are thought by some to be divergent and unphysical, renormalized parameters are finite and measurable, and the need for delicate cancellations between the renormalized Higgs mass parameter and EFT matching corrections is therefore considered by some to constitute a more salient formulation of the Higgs naturalness problem. Here, we argue that to the contrary, the need for fine tuning of the renormalized Higgs mass parameter is an eliminable, unphysical artifact of renormalization scheme, and that this severely weakens the grounds for regarding it as a problematic instance of fine tuning. In doing so, we highlight what we take to be a number of important conceptual lessons about the physical interpretation of model parameters in QFT.

Higgsino dark matter in an economical Scherk-Schwarz setup

We consider a minimal natural supersymmetric model based on an extra dimension with supersymmetry breaking provided by the Scherk-Schwarz mechanism. The lightest supersymmetric particle is a neutral, quasi-Dirac Higgsino and, unlike in previous studies, we assume that all Standard Model fields are propagating in the bulk. The resulting setup is minimal, as neither extra matter, effective operators, nor extra $U(1)$ groups are needed in order to be viable. The model has three free parameters which are fixed by the Higgsino mass -- set to the range 1.1-1.2 TeV so it can play the role of Dark Matter, and by the requirements of correct electroweak breaking and the mass of the Higgs. After imposing the previous conditions we find a benchmark scenario that passes all experimental constrains with an allowed range for the supersymmetric parameters. In particular we have found gluinos in the range 2.0-2.1 TeV mass, electroweakinos and sleptons almost degenerate in the range 1.7-1.9 TeV and squarks degenerate in the range 1.9-2.0 TeV. The best discovery prospects are: i.) gluino detection at the high luminosity LHC ($\gtrsim 3\, \text{ab}^{-1}$), and ii.) Higgsino detection at next-generation dark matter direct detection experiments. The model is natural, as the fine-tuning for the fixed values of the parameters is moderate mainly because supersymmetry breaking parameters contribute linearly to the Higgs mass parameter, rather than quadratically as in most models.

Global aspects of the renormalization group and the hierarchy problem

The discovery of the Higgs boson by the ATLAS and CMS collaborations allowed us to precisely determine its mass being 125.09±0.24 GeV. This value is intriguing as it lies at the frontier between the regions of stability and meta-stability of the standard model vacuum. It is known that the hierarchy problem can be interpreted in terms of the near criticality between the two phases. The coefficient of the Higgs bilinear in the scalar potential, m2, is pushed by quantum corrections away from zero, towards the extremes of the interval [−MPl2,MPl2] where MPl is the Planck mass. In this article, I show that demanding topological invariance for the renormalisation group allows us to extend the beta functions such that the particular value of the Higgs mass parameter observed in our universe regains naturalness. In holographic terms, invariance to changes of topology in the bulk is dual to a natural large hierarchy in the boundary quantum field theory. The demand of invariance to topology changes in the bulk appears to be strongly tied to the invariance of string theory to T-duality in the presence of H-fluxes.

Radiative electroweak symmetry breaking in standard model extensions

We study the possibility of radiative electroweak symmetry breaking where loop corrections to the mass parameter of the Higgs boson trigger the symmetry breaking in various extensions of the Standard Model (SM). Although the mechanism fails in the SM, it is shown to be quite successful in several extensions which share a common feature of having an additional scalar around the TeV scale. The positive Higgs mass parameter at a high energy scale is turned negative in the renormalization group flow to lower energy by the cross couplings between the scalars in the Higgs potential. The type-II seesaw model with a TeV scale weak scalar triplet, a two-loop radiative neutrino mass model with new scalars at the TeV scale, the inert doublet model, scalar singlet dark matter model, and a universal seesaw model with an additional U(1) broken at the TeV scale are studied and shown to exhibit successful radiative electroweak symmetry breaking.

UV complete partially composite pseudo-Nambu Goldstone boson Higgs

We explore an electroweak symmetry breaking (EWSB) scenario based on the mixture of a fundamental Higgs doublet and an SU(4)/Sp(4) composite pseudo-Nambu-Goldstone doublet---a particular manifestation of bosonic technicolor/induced EWSB. Taking the fundamental Higgs mass parameter to be positive, EWSB is triggered by the mixing of the doublets. This setup has several attractive features and phenomenological consequences, which we highlight: (i) Unlike traditional bosonic technicolor models, the hierarchy between ${\mathrm{\ensuremath{\Lambda}}}_{\mathrm{TC}}$ and the electroweak scale depends on vacuum (mis)alignment and can be sizable, yielding an attractive framework for natural EWSB; (ii) As the strong sector is based on SU(4)/Sp(4), a fundamental (UV-complete) description of the strong sector is possible, that is informed by the lattice; (iii) The lightest vector resonances occur in the 10-plet, 5-plet and singlet of Sp(4). Misalignment leads to a 10-plet ``parity-doubling'' cancellation in the $S$ parameter, and a suppressed 5-plet contribution; (iv) Higgs coupling deviations are typically of $\mathcal{O}(1%)$; (v) The 10-plet isotriplet resonances decay dominantly to a massive technipion and a gauge boson, or to technipion pairs, rather than to gauge boson or fermion pairs; moreover, their couplings to fermions are small. Thus, the bounds on this setup from conventional heavy-vector-triplet searches are weak. A supersymmetric $U(1{)}_{R}$ symmetric realization is briefly described.

Naturalness made easy: two-loop naturalness bounds on minimal SM extensions

The main result of this paper is a collection of conservative naturalness bounds on minimal extensions of the Standard Model by (vector-like) fermionic or scalar gauge multiplets. Within, we advocate for an intuitive and physical concept of naturalness built upon the renormalisation group equations. In the effective field theory of the Standard Model plus a gauge multiplet with mass M , the low scale Higgs mass parameter is a calculable function of overline{mathrm{MS}} input parameters defined at some high scale Λh> M . If the Higgs mass is very sensitive to these input parameters, then this signifies a naturalness problem. To sensibly capture the sensitivity, it is shown how a sensitivity measure can be rigorously derived as a Bayesian model comparison, which reduces in a relevant limit to a Barbieri-Giudice-like fine-tuning measure. This measure is fully generalisable to any perturbative EFT. The interesting results of our two-loop renormalisation group study are as follows: for Λh = ΛPl we find “10% fine-tuning” bounds on the masses of various gauge multiplets of M<mathcal{O}left(1-10right) TeV, with bounds on fermionic gauge multiplets significantly weaker than for scalars; these bounds remain finite in the limit Λh → M+, weakening to M<mathcal{O}left(1-100right) TeV; and bounds on coloured multiplets are no more severe than for electroweak multiplets, since they only directly correct the Higgs mass at three-loop.

Solving the Hierarchy Problem at Reheating with a Large Number of Degrees of Freedom.

We present a new solution to the electroweak hierarchy problem. We introduce N copies of the standard model with varying values of the Higgs mass parameter. This generically yields a sector whose weak scale is parametrically removed from the cutoff by a factor of 1/sqrt[N]. Ensuring that reheating deposits a majority of the total energy density into this lightest sector requires a modification of the standard cosmological history, providing a powerful probe of the mechanism. Current and near-future experiments can explore much of the natural parameter space. Furthermore, supersymmetric completions that preserve grand unification predict superpartners with mass below m_{W}M_{pl}/M_{GUT}∼10 TeV.

Natural supersymmetry from extra dimensions

We show that natural supersymmetry can be embedded in a five-dimensional theory with supersymmetry breaking \`a la Scherk-Schwarz (SS). There is no 'gluino-sucks' problem for stops localized in the four-dimensional brane and gluinos propagating in the full five-dimensional bulk, and sub-TeV stops are easily accommodated. The $\mu / B_\mu$ problem is absent as well; the SS breaking generates a Higgsino Dirac mass and no bilinear Higgs mass parameter in the superpotential is required. Moreover, for non-maximal SS twists leading to $\tan \beta \simeq 1$, the Higgs spectrum is naturally split, in agreement with LHC data. The 125-GeV Higgs mass and radiative electroweak symmetry breaking can be accommodated by minimally extending the Higgs sector with $Y=0$ $SU(2)_L$ triplets.