Coset SO Research Articles

Composite resonances at a 10 TeV muon collider

We investigate the reach for resonances of the composite Higgs models at a 10 TeV μ+μ− collider with up to 10 ab−1 luminosity. The strong dynamics sector is modeled by the minimal coset SO(5)/SO(4), where vector resonances are in (3, 1) of SO(4) and fermions are in (2, 2). Various production and decay channels are studied. For the spin-1 resonances, the projections are made based on the radiative return and vector boson fusion production channels. The muon collider can cover most of the kinematically allowed mass range and can measure the coupling gρ to percent level. For the fermionic resonances (i.e. the top partners), pair production easily covers the resonance mass below 5 TeV, while single production extends the reach to 6 TeV for a small ξ = 0.015.

Open F-branes

We include in F-theory, through open Type I F-theory branes (F-branes), string theories with N = 1 supersymmetry, both Type I and heterotic. Type I branes are distinguished from Type II by worldvolume parity projection. The same open Type I branes describe both open Type I superstrings and closed heterotic upon different sectionings from F-branes to worldsheets, while closed Type I superstrings arise from closed Type I branes. (Type II superstrings come from closed Type II branes, as described previously.)F-theory manifests the exceptional-group U-duality symmetry, with all massless bosonic fields in a single gauge coset. This coset branches to the usual bosonic supergravity fields upon sectioning. We examine in detail the simple case of D = 3 F-theory: parity projection reduces the Type II coset SL(5)/SO(3,2) to the Type I coset SO(3,3)/SO(2,1)2 = SL(4)/SO(2,2).

Dimensional reduction of higher derivative heterotic supergravity

Higher derivative couplings of hypermultiplets to 6D, N = (1, 0) supergravity are obtained from dimensional reduction of 10D heterotic supergravity that includes order α′ higher derivative corrections. Reduction on T4 is followed by a consistent truncation. In the resulting action the hyperscalar fields parametrize the coset SO(4, 4)/(SO(4) × SO(4)). While the SO(4, 4) symmetry is ensured by Sen’s construction based on string field theory, its emergence at the field theory level is a nontrivial phenomenon. A number of field redefinitions in the hypermultiplet sector are required to remove several terms that break the SO(4) × SO(4) down to its SO(4) diagonal subgroup in the action and the supersymmetry transformation rules. Working with the Lorentz Chern-Simons term modified 3-form field strength, where the spin connection has the 3-form field strength as torsion, is shown to simplify considerably the dimensional reduction.

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.

Composite dynamics in the early Universe

We study the occurrence of a strong first-order electroweak phase transition in composite Higgs models. Minimal constructions realising this scenario are based on the coset SO(6)/SO(5) which delivers an extended Higgs sector with an additional scalar. In such models, a two-step phase transition can be obtained with the scalar singlet acquiring a vacuum expectation value at intermediate temperatures. A bonus of the Nambu-Goldstone boson nature of the scalar-sector dynamics is the presence of non-renormalisable Higgs in- teractions that can trigger additional sources of CP violation needed to realise baryogenesis at the electroweak scale. Another interesting aspect of this scenario is the generation of gravitational wave signatures that can be observed at future space-based interferometers.

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.

Prospects of searching for composite resonances at the LHC and beyond

Composite Higgs models predict the existence of resonances. We study in detail the collider phenomenology of both the vector and fermionic resonances, including the possibility of both of them being light and within the reach of the LHC. We present current constraints from di-boson, di-lepton resonance searches and top partner pair searches on a set of simplified benchmark models based on the minimal coset SO(5)/SO(4), and make projections for the reach of the HL-LHC. We find that the cascade decay channels for the vector resonances into top partners, or vice versa, can play an important role in the phenomenology of the models. We present a conservative estimate for their reach by using the same-sign di-lepton final states. As a simple extrapolation of our work, we also present the projected reach at the 27 TeV HE-LHC and a 100 TeV pp collider.

Constraining composite Higgs models using LHC data

We systematically study the modifications in the couplings of the Higgs boson, when identified as a pseudo Nambu-Goldstone boson of a strong sector, in the light of LHC Run 1 and Run 2 data. For the minimal coset SO(5)/SO(4) of the strong sector, we focus on scenarios where the standard model left- and right-handed fermions (specifically, the top and bottom quarks) are either in 5 or in the symmetric 14 representation of SO(5). Going beyond the minimal 5L − 5R representation, to what we call here the ‘extended’ models, we observe that it is possible to construct more than one invariant in the Yukawa sector. In such models, the Yukawa couplings of the 125 GeV Higgs boson undergo nontrivial modifications. The pattern of such modifications can be encoded in a generic phenomenological Lagrangian which applies to a wide class of such models. We show that the presence of more than one Yukawa invariant allows the gauge and Yukawa coupling modifiers to be decorrelated in the ‘extended’ models, and this decorrelation leads to a relaxation of the bound on the compositeness scale (f ≥ 640 GeV at 95% CL, as compared to f ≥ 1 TeV for the minimal 5L − 5R representation model). We also study the Yukawa coupling modifications in the context of the next-to-minimal strong sector coset SO(6)/SO(5) for fermion-embedding up to representations of dimension 20. While quantifying our observations, we have performed a detailed χ2 fit using the ATLAS and CMS combined Run 1 and available Run 2 data.

Electroweak symmetry breaking and collider signatures in the next-to-minimal composite Higgs model

We conduct a detailed numerical analysis of the composite pseudo-Nambu-Goldstone Higgs model based on the next-to-minimal coset SO(6)/SO(5) ≅ SU(4)/Sp(4), featuring an additional SM singlet scalar in the spectrum, which we allow to mix with the Higgs boson. We identify regions in parameter space compatible with all current exper-imental constraints, including radiative electroweak symmetry breaking, flavour physics, and direct searches at colliders. We find the additional scalar, with a mass predicted to be below a TeV, to be virtually unconstrained by current LHC data, but potentially in reach of run 2 searches. Promising indirect searches include rare semi-leptonic B decays, CP violation in Bs mixing, and the electric dipole moment of the neutron.

Coset construction of AdS particle dynamics

We analyze the dynamics of the AdSN+1 particle realized on the coset SO(2, N)/SO (1,N). Hamiltonian reduction provides the physical phase space in terms of the coadjoint orbit obtained by boosting a timelike element of 𝔰𝔬(2, N). We show equivalence of this approach to geometric quantization and to the SO(N) covariant oscillator description, for which the boost generators entail a complicated operator ordering. As an alternative scheme, we introduce dual oscillator variables and derive their algebra at the classical and the quantum levels. This simplifies the calculations of the commutators for the boost generators and leads to unitary irreducible representations of 𝔰𝔬(2, N) for all admissible values of the mass parameter. We furthermore discuss an SO(N) covariant supersymmetric extension of the oscillator quantization, with its realization for superparticles in AdS2 and AdS3 given by recent works.

Extending the analysis of electroweak precision constraints in composite Higgs models

In this paper we present a detailed analysis of the Electroweak Precision Observables (EWPO) in composite Higgs models based on the coset SO(5)/SO(4). In our study we include both the fermionic top partners and the spin-1 resonances and consider their possible interplay as well. In order to achieve calculability we use the assumptions of i) partial Ultra Violet Completion (PUVC) following [1] and, ii) absence of sizable effects from physics above the cut-off. Apart from the EWPO, we also take into account the constraints from the top quark, Z and the Higgs boson masses whenever they can be predicted in terms of the model parameters. After presenting our analytic results (often, in certain limits) and discussing their symmetry properties, we also perform detailed fits of the model parameters following the Bayesian approach. We show the posterior probability distributions of the parameters in various scenarios and provide with analytic understanding whenever possible. We find that in certain cases the EWPO allow the compositeness scale to lie well below 1 TeV. Moreover, fermionic top partners of mass around 1 TeV and spin-1 resonances of mass around 2–3 TeV are consistent with the precision data.

Orbit method quantization of the AdS2 superparticle

We consider the Hamiltonian reduction and canonical quantization of a massive AdS2 superparticle realized on the coset SO(1,1). The phase space of the massive superparticle is represented as a coadjoint orbit of a timelike element of . This orbit has a well defined symplectic structure and the symmetry is realized as the Poisson bracket algebra of the Noether charges. We then construct canonical coordinates given by one bosonic and one fermionic oscillator, whose quantization leads to the Holstein–Primakoff type realization of . We also perform a similar analysis and discuss new features and inconsistencies in the massless case.

Pizzetti Formulae for Stiefel Manifolds and Applications

Pizzetti's formula explicitly shows the equivalence of the rotation invariant integration over a sphere and the action of rotation invariant differential operators. We generalize this idea to the integrals over real, complex, and quaternion Stiefel manifolds in a unifying way. In particular we propose a new way to calculate group integrals and try to uncover some algebraic structures which manifest themselves for some well-known cases like the Harish-Chandra integral. We apply a particular case of our formula to an Itzykson-Zuber integral for the coset SO(4)/[SO(2)xSO(2)]. This integral naturally appears in the calculation of the two-point correlation function in the transition of the statistics of the Poisson ensemble and the Gaussian orthogonal ensemble in random matrix theory.

A systematic approach to the SILH Lagrangian

We consider the electroweak chiral Lagrangian, including a light scalar boson, in the limit of small ξ=v2/f2. Here v is the electroweak scale and f is the corresponding scale of the new strong dynamics. We show how the conventional SILH Lagrangian, defined as the effective theory of a strongly-interacting light Higgs (SILH) to first order in ξ, can be obtained as a limiting case of the complete electroweak chiral Lagrangian. The approach presented here ensures the completeness of the operator basis at the considered order, it clarifies the systematics of the effective Lagrangian, guarantees a consistent and unambiguous power counting, and it shows how the generalization of the effective field theory to higher orders in ξ has to be performed. We point out that terms of order ξ2, which are usually not included in the SILH Lagrangian, are parametrically larger than terms of order ξ/16π2 that are retained, as long as ξ≳1/16π2. Conceptual issues such as custodial symmetry and its breaking are also discussed. For illustration, the minimal composite Higgs model based on the coset SO(5)/SO(4) is considered at next-to-leading order in the chiral expansion. It is shown how the effective Lagrangian for this model is contained as a special case in the electroweak chiral Lagrangian based on SU(2)L⊗SU(2)R/SU(2)V.

Phenomenological aspects of supersymmetric composite Higgs models

We study previously introduced models of pseudo--Nambu-Goldstone boson Higgs from linearly realized minimal coset SO(5)/SO(4) and matter in the fundamental in supersymmetric theories. Partial compositeness is at work for top and electroweak gauge fields. New states potentially relevant for LHC signatures are identified and we show how to reinterpret existing experimental results as exclusion bounds. The lightest colored particles, with a mass below the TeV, are fermionic and scalars top partners. We outline a viable mechanism originating masses of other standard model quarks: they result from the generation of dimension five operators in a nonminimal flavor violating context. We study the impact of such operators on flavor processes and we show how experimental bounds are satisfied.

Hunting composite vector resonances at the LHC: naturalness facing data

We introduce a simplified low-energy effective Lagrangian description of the phenomenology of heavy vector resonances in the minimal composite Higgs model, based on the coset SO(5)/SO(4), analysing in detail their interaction with lighter top partners. Our construction is based on robust assumptions on the symmetry structure of the theory and on plausible natural assumptions on its dynamics. We apply our simplified approach to triplets in the representations (3, 1) and (1, 3) and to singlets in the representation (1, 1) of SO(4). Our model captures the basic features of their phenomenology in terms of a minimal set of free parameters and can be efficiently used as a benchmark in the search for heavy spin-1 states at the LHC and at future colliders. We devise an efficient semi-analytic method to convert experimental limits on {\sigma} {\times} BR into bounds on the free parameters of the theory and we recast the presently available 8 TeV LHC data on experimental searches of spin-1 resonances as exclusion regions in the parameter space of the models. These latter are conveniently interpreted as a test of the notion of naturalness.

Composite dark matter and LHC interplay

The actual realization of the electroweak symmetry breaking in the context of a natural extension of the Standard Model (SM) and the nature of Dark Matter (DM) are two of the most compelling questions in high-energy particle physics. Composite Higgs models may provide a unified picture in which both the Higgs boson and the DM particle arise as pseudo Nambu-Goldstone bosons of a spontaneously broken global symmetry at a scale $f\sim$ TeV. In this paper we analyze a general class of these models based on the coset SO(6)/SO(5). Assuming the existence of light and weakly coupled spin-1 and spin-1/2 resonances which mix linearly with the elementary SM particles, we are able to compute the effective potential of the theory by means of some generalized Weinberg sum rules. The properties of the Higgs boson, DM, top quark and the above resonances are thus calculable and tightly connected. We perform a wide phenomenological analysis, considering both collider physics at the LHC and astrophysical observables. We find that these models are tightly constrained by present experimental data, which are able to completely exclude the most natural setup with $f\simeq 800$ GeV. Upon increasing the value of $f$, an allowed region appears. In particular for $f\simeq 1.1$ TeV we find a concrete realization that predicts $m_{DM}\simeq 200$ GeV for the DM mass. This DM candidate lies close to the present sensitivity of direct detection experiments and will be ruled out - or discovered - in the near future.

Dynamical twisting and the b ghost in the pure spinor formalism

After adding an RNS-like fermionic vector ψ m to the pure spinor formalism, the non-minimal b ghost takes a simple form similar to the pure spinor BRST operator. The N=2 superconformal field theory generated by the b ghost and the BRST current can be interpreted as a “dynamical twisting” of the RNS formalism where the choice of which spin $ \frac{1}{2} $ ψ m variables are twisted into spin 0 and spin 1 variables is determined by the pure spinor variables that parameterize the coset SO(10)/U(5).

Implications of a light Higgs in composite models

Abstract We study the Higgs mass in composite Higgs models with partial compositeness, extending the results of ref. [1] to different representations of the composite sector for SO(5)/SO(4) and to the coset SO(6)/SO(5). For a given tuning we find in general a strong correlation between the mass of the top partners and the Higgs mass, akin to the one in supersymmetry. If the theory is natural a Higgs mass of 125 GeV typically requires fermionic partners below TeV which might be within the reach of the present run of LHC. A discussion of CP properties of both cosets is also presented.

On the effect of resonances in composite Higgs phenomenology

We consider a generic composite Higgs model based on the coset SO(5)/SO(4) and study its phenomenology beyond the leading low-energy effective lagrangian approximation. Our basic goal is to introduce in a controllable and simple way the lowest-lying, possibly narrow, resonances that may exist is such models. We do so by proposing a criterion that we call partial UV completion. We characterize the simplest cases, corresponding respectively to a scalar in either singlet or tensor representation of SO(4) and to vectors in the adjoint of SO(4). We study the impact of these resonances on the signals associated to high-energy vector boson scattering, pointing out for each resonance the characteristic patterns of depletion and enhancement with respect to the leading-order chiral lagrangian. En route we derive the O(p 4) general chiral lagrangian and discuss its peculiar accidental and approximate symmetries.