Massless composites with massive constituents

We construct model field theories in which a confining gauge interaction binds massive elementary fermions into massless composite particles. The massless composites are either Goldstone bosons or $\text{spin}\text{-}\text{1}\text{2}$ fermions. In these models, the manner in which exact chiral symmetries are realized changes at a critical value of the elementary fermion mass of order (e²/16π²)Λ, where Λ is the confinement scale and e is a weak gauge coupling.     

A low composite scale preon model with complementarity

We have constructed the first “realistic candidate” preon model with low composite scale satisfying complementarity between the Higgs and confining phases. The model is based onSU(4) metacolor and predicts four generations of ordinary quarks and leptons together with heavy neutrinos at the level of the standard gauge groupSU(3) _c ×SU(2) _L ×U(1) _Y . There are no exotic massless fermions. The global family group isSU(2)×U(1).     

A dynamical theory for the rishon model

We propose a composite model for quarks and leptons based on an exact SU(3)_C × SU(3)_H gauge theory and two fundamental $\text{J=}\text{1}\text{2}$ fermions: a charged T-rishon and a neutral V-rishon. Quarks, leptons and W-bosons are SU(3)_H-singlet composites of rishons. A dynamically broken effective SU(3)_C × SU(2)_L × SU(2)_R × U(1)_B?L gauge theory emerges at the composite level. The theory is “natural”, anomaly free, has no fundamental scalar particles, and describes at least three generations of quarks and leptons.     

On the excited quarks and leptons

Using a duality-like finite energy sum rule, we discuss the assumption of having excited fermions at the W scale in a supersymmetric(SUSY) and non-supersymmetric hypercolour theory where quarks and leptons are bound states of fermion and scalar preon constituents. We conclude that a SUSY-like composite model cannot have excited fermions having a mass smaller than 0.5 TeV. A non-SUSY composite model having composite fermions but elementary W bosons can produce an excited fermion mass of the order of M_W provided that the scalar vacuum condensate is of the order of the (TeV)² scale of compositeness.     

THE COMPOSITE MODEL OF LEPTON AND QUARK WITH ONLY ONE CONSTITUENT SCALAR

We propose a composite model of leptons and quarks containing two constituent fermions of spin 1/2 and a constituent scalar. The constituent fermions are massless and color singlets. Leptons, quarks and weak vector bosons are composites confined by SU(3)_H local gauge interaction, where leptons are made of three constituent fermions and quarks are two-body composites of a scalar and a fermion. The number of the constituent particles is less in our model. There are less exotic leptons and quarks. Quark-lepton parallelism holds. Weak interactions appear only at the composite level as residual short-range interactions among hypercolor singlets. The violation of parity occurs by the mechanism of dynamical symmetry breaking.     

Role of quantum statistics in multi-particle decay dynamics

The role of quantum statistics in the decay dynamics of a multi-particle state, which is suddenly released from a confining potential, is investigated. For an initially confined double particle state, the exact dynamics is presented for both bosons and fermions. The time-evolution of the probability to measure two-particle is evaluated and some counterintuitive features are discussed. For instance, it is shown that although there is a higher chance of finding the two bosons (as oppose to fermions, and even distinguishable particles) at the initial trap region, there is a higher chance (higher than fermions) of finding them on two opposite sides of the trap as if the repulsion between bosons is higher than the repulsion between fermions. The results are demonstrated by numerical simulations and are calculated analytically in the short-time approximation. Furthermore, experimental validation is suggested.     

The N = 4 supersymmetric E8 gauge theory and coset space dimensional reduction

Reasons are given to suggest that the N = 4 supersymmetric E₈ gauge theory be considered as a serious candidate for a physical theory. The symmetries of this theory are broken by a scheme based on coset space dimensional reduction. The resulting theory possesses four conventional generations of low-mass fermions together with their mirror particles.     

Generations of massless composite quarks and leptons

We present a QCD-like composite model in which quarks, leptons and technifermions are three-body systems made out of three kinds of massless elementary fermions t, c and w, each carrying technicolor, color and weak gauge interactions, respectively. Discrete symmetries, remnants of the U(1)_A of the original lagrangian, are responsible for the masslessness of all the quarks and leptons and give the precise meaning of the generations. The model exhibits three generations for both quarks and leptons. Small but non-zero masses of the quarks and leptons are produced by the technicolor condensate of the composite technifermions, which thereby leads to the non-trivial Cabibbo mixing. Proton decays are all forbidden at the mass scale of the QCD-like theory.     

AN SU(6) GRAND UNIFIED MODEL

A model of grand unified theory based on SU(6) gauge group is proposed. It can accommodate two generations of ordinary fermions with V－A weak coupling and two generations of anomalous fermions with V+A weak coupling. In this model a new discrete symmetry is introduced which insures existence of fermions with lower masses when SU(6) gauge symmetry is spontaneously broken. We choose simple Higgs fields with appropriate vacuum expectation values so that the masses of anomalous fermions are heavier than those of ordinary fermions. This model also gives the same value of Weinberg angle, sin²θw=3/8, as in the usual SU(5) grand unified model at the grand unified scale.     

Composite fermions,trios, and quartets in the Fermi-Bose mixture of neutral particles

We consider the model of a Fermi-Bose mixture with strong hard-core repulsion between particles of the same sort and attraction between particles of different sorts. In this case, in addition to the standard anomalous averages of the type 〈b〉, 〈bb〉, and 〈cc〉, pairing between fermions and bosons of the type 〈bc〉 is possible. This pairing corresponds to creation of composite fermions in the system. At low temperatures and equal densities of fermions and bosons, composite fermions are further paired into quartets. At higher temperatures, trios consisting of composite fermions and elementary bosons are also present in the system. Our investigations are important in connection with the recent observation of weakly bound dimers in magnetic and optical dipole traps at ultralow temperatures and with the observation of collapse of a Fermi gas in an attractive Fermi-Bose mixture of neutral particles.     

Towards a realistic composite model of quarks and leptons

Within the context of the 't Hooft anomaly matching scheme, some guiding principles for model building are discussed with an eye to low-energy phenomenology. It is argued that Λ_ch (chiral symmetry breaking scale of the global color-flavor group G_CF) ≈ Λ_MC (metacolor scale) and Λ_gCF (unification scale of the gauge subgroup of G_CF) ≲ Λ_ch. As illustrations of the method, two composite models are suggested that can give rise to three or four generations of ordinary quarks and leptons without exotic fermions.     

Cosmological consequences of grand unification beyond SU(5)

We examine the cosmological consequences of new types of fermions generally present in GUTs based on unitary groups larger than SU(5) which break down to SU(5) at ultralarge energies. We find that some SU(5) singlet fermions in such theories tend to have masses small compared to 10¹⁵ GeV. If sufficiently light (or massless) such particles affect He abundance unacceptably. If heavier (but still light compared to 10¹⁵ GeV) the decays of such particles generate entropy and thus greatly suppress n_B/n_γ.Such theories also contain ultraheavy fermions. Their decays are shown to be a prime source of singlet fermions. It is also shown that the decays of ultraheavy fermions generate entropy which tends to suppress the contribution to n_B/n_γ from usual mechanisms. These decays may themselves, however, generate a baryon asymmetry.     

Anomalous moments of heavy charged leptons

If leptons and quarks are composite particles we expect them to have anomalous moments: an anomalous magnetic moment and an analogue of this with respect to the weak neutral current. If these moments are suppressed by chiral symmetry they will have sizeable values only for heavy fermions, e.g. for fermions of the fourth generation. The forward-backward asymmetry of e⁺e⁻ → f̄f on the Z⁰ resonance is particularly suited for detecting the anomalous “weak magnetic” moment of f if f is the charged lepton of the fourth generation. Under favourable circumstances this moment may lead to a 10% effect.     

Induced p-wave superfluidity in two dimensions: Brane world in cold atoms and nonrelativistic defect CFTs

We propose to use a two-species Fermi gas with the interspecies s-wave Feshbach resonance to realize p-wave superfluidity in two dimensions. By confining one species of fermions in a two-dimensional plane immersed in the background three-dimensional Fermi sea of the other species, an attractive interaction is induced between two-dimensional fermions. We compute the pairing gap in the weak-coupling regime and show that it has the symmetry of p_x+ip_y. Because the magnitude of the pairing gap increases toward the unitarity limit, it is possible that the critical temperature for the p_x+ip_y-wave superfluidity becomes within experimental reach. The resulting system has a potential application to topological quantum computation using vortices with non-Abelian statistics. We also discuss aspects of our system in the unitarity limit as a “nonrelativistic defect conformal field theory (CFT)”. The reduced Schrödinger algebra, operator-state correspondence, scaling dimensions of composite operators, and operator product expansions are investigated.     

Hierarchy of composite fermions in the Hamiltonian theory

Most states of the fractional quantum Hall effect may be interpreted in terms of an integral quantum Hall effect of weakly-interacting quasiparticles (composite fermions). The recently discovered state does not belong to these states because its formation is due to the residual interactions between composite fermions, which become relevant when the composite-fermion levels are only partially filled. We have derived a model of interacting composite fermions, which reveals the self-similarity of the fractional quantum Hall effect and which allows for a systematic study of higher generations of composite fermions. Here, we derive the form of the interaction potential between these hierarchical composite fermions and provide some stability criteria for such states.     

Split light composite supermultiplets

The splitting induced by soft supersymmetry (SUSY) breaking inside the light composite supermultiplets of confining SUSY gauge theories is studied by effective lagrangian methods. Examples with and without unbroken chiral symmetries are considered. In the former case, for a suitable breaking, the lightest states are $\text{spin}\text{-}\text{1}\text{2}$ fermions. A prototype model for one leptonic family is discussed.     

Quarks and leptons

We review the physics of quarks and leptons within the framework of gauge theories for the weak and electromagnetic interactions. The Weinberg-Salam SU(2) × U(1) theory is used as a “reference point” but models based on larger gauge groups, especially SU(2)_L × SU(2)_R × U(1), are discussed. We distinguish among thre “generations” of fundamental fermions: The first generation (e^?, ν_e, u, d), the second generation (μ^?, ν_μ, c, s) and the third generation (τ^?, ν_τ, t, b). For each generation we discuss the classification of all fermions, the charged and neutral weak currents, possible right-handed currents, parity and CP-violation, fermion masses and Cabibbo-like angles and related problems. We review theoretical ideas as well as experimental evidence, emphasizing open theoretical problems and possible experimental tests. The possibility of unifying the weak, electromagnetic and strong interactions in a grand unification scheme is reviewed. The problems and their possible solutions are presented, generation by generation, but a brief subject-index (following the table of contents) enables the interested reader to follow any specific topic throughout the three generations.     

Radiative decays of quarkonia into Goldstone fermions

We consider the decay of³ S ₁ quarkonia into a photon and two Goldstone fermions in a model realizing supersymmetry in a nonlinear way. We derive a lower bound of 3.5 GeV for the scale of spontaneous supersymmetry breaking from Υ-decays. We show that the decay of a³ S ₁ quarkonium into two Goldstone fermions is forbidden in the order we consider.     

AN SO(12) GRAND UNIFLIED MODEL

Assignment of the two "twins" generations of fermions in a SO(12) 32-dimensional spinor representation and its conjugate representation is given. Mass spectrum of fermions and their Cabibbo angles are discussed. The assignment of the four generations of fermions in a 352-dimensional spinor-tensor representaion of SO(12) Without repetiton is briefly discussed.     

The Relation of Constraints on Particle Statistics for Different Species of Particles

Quons are particles characterized by the parameter q, which permits smooth interpolation between Bose and Fermi statistics; q = 1 gives bosons, q = -1 gives fermions. In this paper we give a heuristic argument for an extension of conservation of statistics to quons with trilinear couplings of the form ffb, where f is fermion-like and b is boson-like. We show that q _f ² = q_b. In particular, we relate the bound on q for photons to the bound on q_e for electrons, allowing the very precise bound for electrons to be carried over to photons. An extension of this argument suggests that all particles are fermions or bosons to a high precision.