Minimal Composite Higgs Model Research Articles

On the importance of three-body decays of vector-like quarks

It is a common feature of vector-like extensions of the electroweak sector to have near degenerate states, such as electroweak doublets. In simplified models, it is usually assumed that these have decay widths saturated by two-body channels. As a consequence, experimental searches can be done focusing on only one of the states of the doublet. Taking as an example case the light exotic electroweak doublet present in the Minimal Composite Higgs Model, we show that including three-body decays in the pair production process makes this separation unfeasible, since both states of the doublet will be present and contribute significantly to the signal. In addition, by recasting present searches in multileptonic channels, with a simplified cut-and-count analysis, a relevant increase in discovery reach or exclusion potential is obtained; this indeed motivates a more detailed analysis. This study shows how an inclusive search strategy, taking into account both the near degeneracy and the presence of three-body decays, will have greater discovery power and be more natural from a model building perspective.

Status of electroweak baryogenesis in minimal composite Higgs

We present an update on the status of electroweak baryogenesis in minimal composite Higgs models. The particularity of this framework is that the electroweak phase transition can proceed simultaneously with the confinement phase transition of the new strong dynamics that produces the composite Higgs. The latter transition is controlled by the dilaton — the pseudo-Goldstone boson of an approximate scale invariance of the composite sector. Since it naturally is first-order, the electroweak phase transition becomes first-order too. Another appealing aspect is that the necessary additional source of CP violation can arise from the variation of the quark Yukawa couplings during the phase transition, which is built-in naturally in this scenario. These two features address the shortcomings of electroweak baryogenesis in the Standard Model. We confront this scenario with the latest experimental bounds derived from collider searches for new resonances and measurements of the Higgs couplings and electric dipole moments. All these constraints provide (or will be able to provide in the near future) important bounds on the considered scenario, with the most stringent ones coming from LHC searches for new resonances which constrain the dilaton mass and couplings. We identify the viable region of parameter space which satisfies all the constraints, and is characterized by a dilaton mass in the 300–500 GeV range and a Higgs decay constant f ≲ 1.1 TeV. We discuss its future tests.

Toward minimal composite Higgs models from regular geometries in bottom-up holography

We study a bottom-up, holographic description of a field theory yielding the spontaneous breaking of an approximate $SO(5)$ global symmetry to its $SO(4)$ subgroup. The weakly coupled, six-dimensional gravity dual has regular geometry. One of the dimensions is compactified on a circle that shrinks smoothly to zero size at a finite value of the holographic direction, hence introducing a physical scale in a way that mimics the effect of confinement in the dual four-dimensional field theory. We study the spectrum of small fluctuations of the bulk fields carrying $SO(5)$ quantum numbers, which can be interpreted as spin-0 and spin-1 bound states in the dual field theory. This work supplements an earlier publication focused only on the $SO(5)$ singlet states. We explore the parameter space of the theory, paying particular attention to composite states that have the right quantum numbers to be identified as pseudo-Nambu-Goldstone bosons (PNGBs). We find that in this model the PNGBs are generally heavy, with masses of the same order as other bound states, indicating the presence of a sizeable amount of explicit symmetry breaking in the field-theory side. Nevertheless, we also find a qualitatively new, unexpected result. When the dimension of the field-theory operator inducing $SO(5)$ breaking is close to half the space-time dimensionality, there exists a region of parameter space in which the PNGBs and the lightest scalar are both parametrically light in comparison to all other bound states of the field theory. Although this region is known to yield metastable classical backgrounds, this finding might be relevant to model building in the composite Higgs context.

Towards top-down holographic composite Higgs: minimal coset from maximal supergravity

Within the context of top-down holography, we study a one-parameter family of regular background solutions of maximal gauged supergravity in seven dimensions, dimensionally reduced on a 2-torus. The dual, four-dimensional confining field theory realises the global (spontaneous as well as explicit) symmetry breaking pattern SO(5) → SO(4). We compute the complete mass spectrum for the fluctuations of the 128 bosonic degrees of freedom of the five-dimensional gravity theory, which correspond to scalar, pseudoscalar, vector, axial-vector, and tensor bound states of the dual field theory, and includes particles with exotic SO(4) quantum numbers. We confirm the existence of tachyonic instabilities near the boundaries of the parameter space.We discuss the interplay between explicit and spontaneous symmetry breaking. The SO(5)/SO(4) coset might provide a first step towards the realisation of a calculable framework and ultraviolet completion of minimal composite Higgs models, if the four pseudo-Nambu-Goldstone bosons are identified with the real components of the Higgs doublet in the standard model (SM), and a subgroup of SO(4) with the SU(2) × U(1) SM gauge group. We exhibit an example with an additional localised boundary term that mimics the effect of a weakly-coupled external sector.

Singlet channel scattering in a composite Higgs model on the lattice

We present the first calculation of the scattering amplitude in the singlet channel beyond QCD. The calculation is performed in SU(2) gauge theory with N_f=2 fundamental Dirac fermions and based on a finite-volume scattering formalism. The theory exhibits a SU(4) rightarrow Sp(4) chiral symmetry breaking pattern that is used to design minimal composite Higgs models currently tested at the LHC. Our results show that, for the range of underlying fermion mass considered, the lowest flavour singlet state is stable.

Flavorful composite Higgs model: Connecting the B anomalies with the hierarchy problem

We present a model which connects the neutral current B anomalies with composite Higgs models. The model is based on the minimal fundamental composite Higgs model with $SU(4)/Sp(4)$ coset. The strong dynamics spontaneously break the symmetry and introduce five Nambu-Goldstone bosons. Four of them become the Standard Model Higgs doublet and the last one, corresponding to the broken local $U(1)'$ symmetry, is eaten by the gauge boson. This leads to an additional TeV-scale $Z'$ boson, which can explain the recent B anomalies. The experimental constraints and allowed parameter space are discussed in detail.

UV completed composite Higgs model with heavy composite partners

We study electroweak symmetry breaking in minimal composite Higgs models $SU(4)/Sp(4)$ with purely fermionic UV completions based on a confining Hypercolor gauge group and find that the extra Higgs potential from the underlying preon mass can destruct the correlation between the mass of Higgs and composite partners. Thus the composite partners can be very heavy for successful electroweak symmetry breaking without enhancing the separation between the new physical scale and Higgs VEV. So this kind of model can be easily realized by ordinary strong dynamics theories without artificial assumptions and more likely consistent with lattice simulations. The UV completion of partial compositeness predicts a light singlet Goldstone boson which interacts with QCD and electroweak gauge bosons through Wess-Zumino-Witten terms. It can be produced through gluon fusion at LHC and decay into gauge boson pairs. We briefly discuss its phenomenology and derive its bounds from LHC searches.

Scattering of Goldstone bosons and resonance production in a composite Higgs model on the lattice

We calculate the coupling between a vector resonance and two Goldstone bosons in SU(2) gauge theory with Nf = 2 Dirac fermions in the fundamental representation. The considered theory can be used to construct a minimal Composite Higgs models. The coupling is related to the width of the vector resonance and we determine it by simulating the scattering of two Goldstone bosons where the resonance is produced. The resulting coupling is gVPP = 7.8 ± 0.6, not far from gρππ ≃ 6 in QCD. This is the first lattice calculation of the resonance properties for a minimal UV completion. This coupling controls the production cross section of the lightest expected resonance at the LHC and enters into other tests of the Standard Model, from Vector Boson Fusion to electroweak precision tests. Our prediction is crucial to constrain the model using lattice input and for understanding the behavior of the vector meson production cross section as a function of the underlying gauge theory. We also extract the coupling {g}_{mathrm{VPP}}^{mathrm{KSRF}} = 9.4 ± 0.6 assuming the vector-dominance and find that this phenomenological estimate slightly overestimates the value of the coupling.

Soft wall holographic model for the minimal composite Higgs boson

We reassess employing the holographic technique to the description of 4D minimal composite Higgs model with $SO(5)\to SO(4)$ global symmetry breaking pattern. The particular 5D bottom-up holographic treatment is inspired by previous work in the context of QCD and it allows to study spin one and spin zero resonances. The resulting spectrum consists of the states transforming under the unbroken $SO(4)$ subgroup and those with quantum numbers in the $SO(5)/SO(4)$ coset. The spin one states are arranged in linear radial trajectories, and the states from the broken subgroup are generally heavier. The spin zero states from the coset space correspond to the four massless Goldstone bosons in 4D. One of them takes the role of the Higgs boson. Restrictions derived from the experimental constraints (Higgs couplings, $S$ parameter, etc.) are then implemented and we conclude that the model is able to accommodate new vector resonances with masses in the range $2$ TeV to $3$ TeV without encountering phenomenological difficulties. The couplings governing the production of these new states in the processes of the SM gauge boson scattering are also estimated. The method can be extended to other breaking patterns.

Probing the top-Higgs sector with composite Higgs models at present and future hadron colliders

We study the production of toverline{t}h and toverline{t} hh at hadron colliders, in the minimal Composite Higgs Models, based on the coset SO(5)/SO(4). We explore the fermionic representations 5 and 14. A detailed phenomenological analysis is performed, covering the energy range of the LHC and its High Luminosity upgrade, as well as that of a future 100 TeV hadron collider. Both resonant and non-resonant production are considered, stressing the interplay and complementary interest of these channels with each other and double Higgs production. We provide sets of representative points with detailed experimental outcomes in terms of modification of the cross sections as well as resonance masses and branching ratios. For non-resonant production, we gauge the relative importance of Yukawa, Higgs trilinear, and contact toverline{t} hh vertices to these processes, and consider the prospect for distinguishing the fermion representations from each other and from the Standard Model. In the production of top partners, we find that the three-body decay channel W+W–t becomes significant in certain regions of parameter space having a degenerate spectrum, and is further enhanced by increasing the top partner’s mass. This motivates both higher energy machines as well as the need to go beyond the current analysis performed for the searches for these resonances.

On the reinterpretation of non-resonant searches for Higgs boson pairs

The detection of production of a pair of Higgs bosons before the end of LHC operation would be a clear evidence of New Physics (NP). As searches for non-resonant production of Higgs pairs are being designed it is of particular importance to be able to conveniently present current experimental results in terms of limits in the most ‘model-independent’ fashion possible. To this end, in this article we provide an analytic parametrization of the differential Higgs-pair production at the LHC in the effective field theory (EFT) extension of the SM. It results from a fit to the theory prediction for the gg → hh cross section at the 13 TeV LHC. Subsequently the resulting formula is used for a reweighing technique that allows to recast exclusion bounds from ATLAS and CMS hh → gamma gamma boverline{b} searches to any point of the considered EFT parameter space. We demonstrate with a fast simulation of the LHC detectors that with this approach it is possible to cover the continuous EFT parameter space, taking correctly into account the efficiencies of signal selections, without the necessity of rerunning a large number of full detector simulations. Finally, the resulting exclusion bounds are confronted with several explicit models, such as setups with additional scalars, including 2HDM, vector-like fermions, and minimal composite Higgs models, which are mapped to the EFT.

Effective field theory perspective on next-to-minimal composite Higgs models

We study both the CP-even and CP-odd effective chiral Lagrangians of next minimal composite Higgs model {with symmetry breaking pattern depicted by the coset $SO(6)/SO(5)$} through the sigma/omega decomposition, in which the Goldstone matrix of the coset is decomposed in terms of the standard model Higgs doublet and an additional scalar singlet $s$ at the electroweak scale. The effective Lagrangian is described by the electroweak chiral Lagrangian up to $p^4$ order, with a function dependence on the Higgs boson and new scalar $s$, named Higgs function. This function in the effective Lagrangian incorporates the Higgs non-linearity or vacuum misalignment effects in the next minimal composite Higgs model, due to the Riemann curvature on the Nambu-Goldstone bosons scalar manifold, leads to various Higgs couplings deviated from the standard model ones, and also indicates the relations among different Higgs couplings in the low energy. Matching to the Higgs effective field theory below the electroweak scale, we obtain various low energy observables such as the electroweak oblique parameters, anomalous triple and quartic gauge couplings, anomalous couplings of Higgs to gauge bosons, in which the Higgs non-linearity effects are encoded in the ratio $\xi\equiv v^2/f^2$ of the electroweak scale and the new physics scale.

Minimal 4D Composite Higgs Models Under Current LHC Constraints

We present preliminary results of the first convergent global fits of several minimal composite Higgs models. Our fits are performed using the differential evolution optimisation package Diver. A variety of physical constraints are taken into account, including a wide range of exclusion bounds on heavy resonance production from Run 2 of the LHC. As a by-product of the fits, we analyse the collider phenomenology of the lightest new up-type and downtype resonances in the viable regions of our models, finding some low-mass resonances that can be probed in future collider searches.

The minimal simple composite Higgs model

Most of the analysis of composite Higgs have focussed on the Minimal Composite Higgs Model, based on the coset SO(5) × U(1)X/ SO(4) × U(1)X. We consider a model based on the coset of simple groups SO(7)/ SO(6), with SO(4) × U(1)X embedded into SO(6). This extension of the minimal model leads to a new complex pNGB that has hypercharge and is a singlet of SU(2)L, with properties mostly determined by the pattern of symmetry breaking and a mass of order TeV. Composite electroweak unification also leads to new bosonic and fermion resonances with exotic charges, not present in the minimal model, the lightest of these resonances being stable. A new rich phenomenology is expected at LHC.

Search for single production of a top quark partner via the T→th and h→WW* channels at the LHC

Many scenarios of physics beyond the Standard Model that address the hierarchy problem also predict the existence of vector-like top quark partners, which are generally expected around the TeV scale. In this paper, we propose to search for a vector-like top quark partner with charge $2/3$ in a simplified model including only two free parameters, the coupling constant $g^{\ast}$ and top quark partner mass $m_T$. We investigate the observability of the top quark partner through the process $pp \to T(\to th)j\to t(\to b W^+\to b \ell^{+} \nu_{\ell})h( \to WW^{\ast}\to \ell^{+}\nu\ell^{-}\bar{\nu}) j$, where $T$ is the heavy top quark partner and $h$ the SM-like Higgs boson, at the Large Hadron Collider (LHC). The discovery prospects and exclusion limits on the parameter plane defined by ($m_T,g^{\ast}$) are obtained for the already scheduled LHC runs as well as at the future High-Luminosity~LHC (HL-LHC). The constraints and projected sensitivities are also interpreted in a realistic model, i.e., the minimal Composite Higgs Model with singlet top quark partners. We finally also analyze the projected sensitivity in terms of the production cross section times branching fraction at the (HL-)LHC.

Exploring fine-tuning of the Next-to-Minimal Composite Higgs Model

We perform a detailed study of the fine-tuning of the two-site, 4D, Next-to-Minimal Composite Higgs Model (NMCHM), based on the global symmetry breaking pattern SO(6) → SO(5). Using our previously-defined fine-tuning measure that correctly combines the effect of multiple sources of fine-tuning, we quantify the fine-tuning that is expected to result from future collider measurements of the Standard Model-like Higgs branching ratios, in addition to null searches for the new resonances in the model. We also perform a detailed comparison with the Minimal Composite Higgs Model, finding that there is in general little difference between the fine-tuning expected in the two scenarios, even after measurements at a high-luminosity, 1 TeV linear collider. Finally, we briefly consider the relationship between fine-tuning and the ability of the extra scalar in the NMCHM model to act as a dark matter candidate, finding that the realisation of a Z2 symmetry that stabilises the scalar is amongst the most natural solutions in the parameter space, regardless of future collider measurements.

Current and future constraints on Higgs couplings in the nonlinear Effective Theory

We perform a Bayesian statistical analysis of the constraints on the nonlinear Effective Theory given by the Higgs electroweak chiral Lagrangian. We obtain bounds on the effective coefficients entering in Higgs observables at the leading order, using all available Higgs-boson signal strengths from the LHC runs 1 and 2. Using a prior dependence study of the solutions, we discuss the results within the context of natural-sized Wilson coefficients. We further study the expected sensitivities to the different Wilson coefficients at various possible future colliders. Finally, we interpret our results in terms of some minimal composite Higgs models.

Topology of electroweak vacua

In the Standard Model, the electroweak symmetry is broken by a complex, SU(2)-doublet Higgs field and the vacuum manifold SU(2)×U(1)/U(1) has the topology of a 3-sphere. We remark that there exist theoretical alternatives that are locally isomorphic, but in which the vacuum manifold is homeomorphic to an arbitrary non-trivial principal U(1)-bundle over a 2-sphere. These alternatives have non-trivial fundamental group and thus feature topologically-stable electroweak strings. An alternative based on the manifold RP3 (with fundamental group Z/2) allows custodial protection of gauge boson masses and their couplings to fermions and has an explicit realisation in the Minimal Composite Higgs Model, in the case of maximal electroweak symmetry breaking. We show that, in common with all alternatives to S3, such models have a problem with fermion masses.

Learning from Higgs physics at future Higgs factories

Future Higgs factories can reach impressive precision on Higgs property measurements. In this paper, instead of conventional focus of Higgs precision in certain interaction bases, we explore its sensitivity to new physics models at the electron-positron colliders. In particular, we study two categories of new physics models, Standard Model (SM) with a real scalar singlet extension, and Two Higgs Double Model (2HDM) as examples of weakly-interacting models, Minimal Composite Higgs Model (MCHM) and three typical patterns of the more general operator counting for strong interacting models as examples of strong dynamics. We perform a global fit to various Higgs search channels to obtain the 95% C.L. constraints on the model parameter space. In the SM with a singlet extension, we obtain the limits on the singlet-doublet mixing angle sin θ, as well as the more general Wilson coefficients of the induced higher dimensional operators. In the 2HDM, we analyze tree level effects in tan β vs. cos(β − α) plane, as well as the one-loop contributions from the heavy Higgs bosons in the alignment limit to obtain the constraints on heavy Higgs masses for different types of 2HDM. In strong dynamics models, we obtain lower limits on the strong dynamics scale. In addition, once deviations of Higgs couplings are observed, they can be used to distinguish different models. We also compare the sensitivity of various future Higgs factories, namely Circular Electron Positron Collider (CEPC), Future Circular Collider (FCC)-ee and International Linear Collider (ILC).

Uncovering new strong dynamics via topological interactions at the 100 TeV collider

In models of composite Higgs dynamics new composite pseudoscalars can interact with the Higgs and electroweak gauge bosons via anomalous interactions, stemming from the topological sector of the underlying theory. We show that a future 100 TeV proton-proton collider (FCC-pp) will be able to test this important sector and thus shed light on the strong dynamics which generates the Higgs and other composite states. To elucidate our results we focus on the topological interactions of a minimal composite Higgs model with a fermionic ultraviolet completion, based on the coset $\text{SU}(4)/\text{Sp}(4)$. We suggest the strategy to test these interactions at the FCC-pp and analyse the expected reach.