Composite Goldstone Bosons Research Articles

Testing the charge-radius coupling of composite Goldstone (Higgs) bosons at hadron colliders

We explore the collider relevance of a charge-radius coupling among light mesons in composite Higgs models. In particular, we focus of a coupling of the photon to the composite Higgs and a composite singlet, arising from isospin violation in the underlying theory. This coupling offers a deep probe of the composite nature of the Higgs mechanism, being sensitive to the electromagnetic and weak isospin structure of its constituents. The main collider effect consists in the production of the Higgs boson in association with a light composite pseudo-scalar. We present an exploratory cut-and-count analysis at hadron colliders, like the LHC, showing that an efficient background suppression can be achieved. More sophisticated techniques, however, are necessary to select a sufficient number of signal events, due to the small production rates. This justifies further investigation of this channel, which is highly complementary to other searches for compositeness in the Higgs sector.

Composite Higgs Models after Run 2

We assess the status of models in which Higgs is a composite pseudo-Nambu Goldstone boson, in the light of the latest 13 TeV Run 2 Higgs data. Drawing from the extensive Composite Higgs literature, we collect together predictions for the modified couplings of Higgs, in particular examining the different predictions for κV and κF. Despite the variety and increasing complexity of models on the market, we point out that many independent models make identical predictions for these couplings. We then look into further corrections induced by tree-level effects such as mass-mixing and singlet VEVs. We then investigate the compatibility of different models with the data, combining Run 1 and recent Run 2 LHC data. We obtain a robust limit on the scale f of 600 GeV, with stronger limits for different choices of fermion embeddings. We also discuss how a deficit in a Higgs channel could pinpoint the type of Composite Higgs model responsible for it.

Nonperturbative analysis of the spectrum of meson resonances in an ultraviolet-complete composite-Higgs model

We consider a vector-like gauge theory of fermions that confines at the multi-TeV scale, and that realizes the Higgs particle as a composite Goldstone boson. The weak interactions are embedded in the unbroken subgroup $Sp(4)$ of a spontaneously broken $SU(4)$ flavour group. The meson resonances appear as poles in the two-point correlators of fermion bilinears, and include the Goldstone bosons plus a massive pseudoscalar $\eta'$, as well as scalars, vectors and axial vectors. We compute the mass spectrum of these mesons, as well as their decay constants, in the chiral limit, in the approximation where the hypercolour $Sp(2N)$ dynamics is described by four-fermion operators, \`a la Nambu-Jona Lasinio. By resumming the leading diagrams in the $1/N$ expansion, we find that the spin-one states lie beyond the LHC reach, while spin-zero electroweak-singlet states may be as light as the Goldstone-boson decay constant, $f\sim 1$ TeV. We also confront our results with a set of available spectral sum rules. In order to supply composite top-quark partners, the theory contains additional fermions carrying both hypercolour and ordinary colour, with an associated flavour symmetry-breaking pattern $SU(6)/SO(6)$. We identify and analyse several non-trivial features of the complete two-sector gauge theory: the 't~Hooft anomaly matching conditions; the higher-dimension operator which incorporates the effects of the hypercolour axial-singlet anomaly; the coupled mass-gap equations; the mixing between the singlet mesons of the two sectors, resulting in an extra Goldstone boson $\eta_0$, and novel spectral sum rules. Assuming that the strength of the four-fermion interaction is the same in the two sectors, we find that the coloured vector and scalar mesons have masses $\gtrsim 4 f$, while the masses of coloured pseudo-Goldstone bosons, induced by gluon loops, are $\gtrsim 1.5f$.

Composite Goldstone dark matter: experimental predictions from the lattice

We study, via first principles lattice simulations, the nonperturbative dynamics of $SU(2)$ gauge theory with two fundamental Dirac flavors. The model can be used simultaneously as a template for composite Goldstone boson dark matter and for breaking the electroweak symmetry dynamically. We compute the form factor, allowing us to estimate the associated electromagnetic charge radius. Interestingly we observe that the form factor obeys vector meson dominance even for the two color theory. We finally compare the model predictions with dark matter direct detection experiments. We find that the composite Goldstone boson dark matter cross sections is constrained by the most stringent direct-detection experiments. Our results are a foundation for quantitative new composite dynamics relevant for model building, and are of interest to current experiments.

Antiferromagnetic gap in the Hubbard model

We compute the temperature-dependence of the antiferromagnetic order parameter and the gap in the two-dimensional Hubbard model at and close to half filling. Our approach is based on truncations of an exact functional renormalization group equation. The explicit use of composite bosonic degrees of freedom permits a direct investigation of the ordered low temperature phase. We show that the Mermin–Wagner theorem is not practically applicable for the spontaneous breaking of the continuous spin symmetry in the antiferromagnetic state. The critical behavior is dominated by the fluctuations of composite Goldstone bosons.

Temperature dependence of antiferromagnetic order in the Hubbard model

We suggest a method for an approximative solution of the two dimensional Hubbard model close to half filling. It is based on partial bosonisation, supplemented by an investigation of the functional renormalisation group flow. The inclusion of both the fermionic and bosonic fluctuations leads in lowest order to agreement with the Hartree-Fock result or Schwinger-Dyson equation and cures the ambiguity of mean field theory . We compute the temperature dependence of the antiferromagnetic order parameter and the gap below the critical temperature. We argue that the Mermin-Wagner theorem is not practically applicable for the spontaneous breaking of the continuous spin symmetry in the antiferromagnetic state of the Hubbard model. The long distance behavior close to and below the critical temperature is governed by the renormalisation flow for the effective interactions of composite Goldstone bosons and deviates strongly from the Hartree-Fock result.

Covariant model of a fermion-antifermion bound state with harmonic confinement.

We solve a covariant equation for a fermion-antifermion system interacting on a three-dimensional hypersurface in Minkowski space for the particular case of a local harmonic-oscillator potential. By assuming free propagation in a perpendicular timelike direction, full covariant bound-state amplitudes are constructed using two different formalisms. We examine and compare the possible suitability of these two approaches for the description of composite Goldstone bosons. The techniques developed are generalizable to other potentials.

HIGGS DOUBLET AS COMPOSITE GOLDSTONE BOSON: CHALLENGE TO MULTI-TEV ENERGY COLLIDERS

The minimum nonlinear extension SU(3)×U(1)/SU(2)×U(1) to the Standard Model, where the Higgs doublet is a composite Goldstone boson, is investigated. The canonical nonlinear realization of the extended symmetry is constructed in the form maximally close to that of the Standard Model. The corresponding most general effective Lagrangian is built. A simplest linear realization of the extended symmetry in an extended fermion sector is found. The Higgs-Goldstone scenario of the electroweak symmetry breaking is outlined from the standpoint of the multi-TeV energy collider phenomenology.

Alternative picture of top quark dynamics

We discuss the possibility that electroweak symmetry is broken dynamically by a condensate of top quarks in a non-bootstrap picture involving a top quark mass m t≈250 GeV but no tightly bound Higgs boson. We show how composite Goldstone bosons are formed as quark-antiquark bound states from a combination of QCD and contact below a scale μ χ = 2 m t , permitting experimental tests of the model near the TeV scale.

Scattering of composite goldstone bosons in a renormalization QFT

We calculate the scattering amplitudes of composite Goldstone bosons in the (2+1)-dimensional four-Fermi model, using the technique of 1/ N expansion. The Goldstone bosons correspond to the symmetry breaking pattern U L( n)×U R( n)→U( n). The effective lagrangian describing the low-energy scattering is explicitly derived. We also compute the effects of explicit symmetry breaking parameters. Unitary in the context of the 1/ N expansion is analyzed in some detail.

Dynamical generation of Majorana masses for gauginos.

It is shown that the exchange of gauge bosons between fermions in a real representation (e.g., the adjoint) produces an attractive force that binds identical fermions into spin-zero Cooper pairs. The condensation of these pairs in the vacuum produces a Majorana mass for the fermions. The associated breaking of fermion number results in a composite Goldstone boson.

Effective lagrangian and mass generation in supersymmetric QCD

We calculate the electromagnetic mass shift of composite Goldstone bosons and quasi-Goldstone fermions in supersymmetric QCD for the case where supersymmetry is explicitly broken by a photino mass term. We use an effective lagrangian approach incorporating the analogues of the ϱ and A 1 vector mesons together with vector meson dominance.

Dynamical gauge symmetry breaking in supersymmetry theories

The supersymmetric extension of the conventional mechanism of dynamical gauge symmetry breaking is presented in the general case where the Goldstone bosons may be either doubled or non-doubled. The models considered are strongly interacting supersymmetric gauge theories with an arbitrary chiral breaking pattern G → H. A subgroup G w of G is weakly gauged and the resulting mass generation mechanisms for the Bose and Fermi gauge fields of G w are analysed. If gauge fields are coupled to non-doubled Goldstone bosons, it is found that supersymmetry is spontaneously broken not just by the masses but also by the spins of the physical particles. The spectrum reveals no supersymmetry multiplet structure. The decoupling of unphysical degrees of freedom is carefully discussed, and the quartet decoupling mechanism is extended to supersymmetry theories with composite Goldstone bosons. The necessary techniques for calculating the masses of pseudo-Goldstone bosons and their supersymmetry partners are demonstrated.

A class of “natural” composite models

The starting point is the attractive class of composite models where quarks and leptons appear as fermion-scalar bound states ( Fφ). The aim is to resolve the “naturality” problem associated with fundamental scalars without losing the appealing properties of Fφ-type composite models. A systematic construction of such models is given, where the scalar constituents automatically qualify as light dynamical scalars, i.e. as composite (pseudo) Goldstone bosons. A comfortably large class of composite models then results, where all standard “naturality” requirements are satisfied: the quark and lepton masses are kept small through 't Hooft's chiral protection mechanism; the dynamical scalar “constituents” are light and the CP problem of QCD finds an automatic solution. Further characteristics are economy, absence of light exotics, possibility of three generations and elegance of anomaly matching. It is shown that existing attractive models with fundamental scalars can be made “natural” in the sense defined above.

Weak interaction symmetry and generation structure in the quasi-Nambu-Goldstone fermion picture of quarks and leptons

We discuss composite models where massless quarks and leptons arise as superpartners of composite Goldstone bosons, resulting from the spontaneous breakdown of global symmetry, in a supersymmetric theory in which the preons are confined by nonabelian hypercolor dynamics. We present different schemes for including the generations. Finally, we note some problems with this approach.

Improved effective-potential formalism for composite fields

We develop an effective-potential formalism for studying dynamical symmetry breaking. The potential that we calculate is single-valued and bounded from below. Our formalism incorporates a stability criterion for deciding whether the broken-symmetry solution to the theory is the physical one. In lowest-order calculations in gauge theories we find that the asymmetric theory will be stable if and only if a composite Goldstone boson can be bound. Our conclusion is that in the weak-coupling approximation there is no dynamical spontaneous breakdown in gauge theories. We then use the renormalization group to argue that if spontaneous breakdown occurs at all, it must also occur for arbitrarily weak coupling. The renormalization group also provides us with evidence that dynamical symmetry breakdown does not occur in infrared-stable theories.