Four families of composite quarks and leptons

Four families of composite quarks and leptons, two standard and two non-standard, are found in a unique solution SU(3)_HC × SU(6)_L × SU(6)_R of a restricted 't Hooft anomaly-matching program. Testable predictions emerge, such as prohibition of μ → eγ, zero charge asymmetry in e⁺e^? → τ⁺τ^? in contrast to e⁺e^? → μ⁺μ^?, and a rich new hadron spectrum masses around M_W. A minimal set of spectator fermions contains color-singlet objects with fractional quark-like charges.     

SU(2) × U(1) breaking by vacuum misalignment

Currently two scenarios exist which explain SU(2) × U(1) breaking: the Higgs mechanism, and standard hypercolor schemes. In this paper, a third scenario called “oblique hypercolor” is proposed. A hyperquark condensate is formed which, although kinematically allowed to point in an SU(2) × U(1) preserving direction, is forced by Yukawa interactions of the hyperquarks to misalign by a small angle, breaking SU(2) × U(1). The low energy spectrum involves normal fermions with correct masses, a partially composite Higgs boson, and physical charged scalars.     

Composite symmetries and sub-constituent models

Assuming the internal A-spin, B-spin and C-spin of particles from basic symmetry SO(4), the color SU(3), horizontal SU(3)', electroweak SU(2)'_w×U(1) and other higher composite symmetries are derived.     

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.     

Composite Higgs scalars

We construct models in which the Higgs doublet whose vacuum expectation breaks SU(2) × U(10 is a bound state of massive strongly interacting fermions. The couplings of the composite Higgs to ordinary fermions are induced by heavy gauge boson exchange in the manner of extended technicolor. Other heavy gauge bosons generate a negative mass term for the Higgs.     

Weak interactions of quasi nambu-goldstone fermions

We investigate the hypothesis that the observed weak interactions are the residual interactions of quasi Goldstone fermions. Left-handed quarks and leptons arise from the spontaneous symmetry breaking U(6) → U(4) × SU(2) in a supersymmetric theory. The simplest preon model realizing this breakdown leads, in the complementary picture, to the supersymmetric extension of the standard model of electroweak interactions. Furthermore, 't Hooft's anomaly conditions are satisfied with respect to the unbroken subgroup of the U(6) flavour symmetry and R-invariance. The preon model predicts the existence of a ninth chiral supermultiplet, the novino.     

Higgs fields and the determination of the Weinberg angle

SU(2) × U(1) gauge theories, in which the Higgs fields transform as doublets under SU(2) are interpreted as pure Yang-Mills theories in six dimensions, the components of the gauge potentials in the extra dimensions playing the role of the Higgs' fields. Two consistent theories are discovered: one in which SU(2) × U(1) is embedded in SU(3) and the vector bosons remain massless - and another where SU(2) × U(1) is embedded in the graded Lie algebra SU(2|1), the symmetry is spontaneously broken in a natural fashion and the theory is equivalent to that of Weinberg and Salam, with a specific value 30° for the Weinberg angle and a prediction of the Higgs' mass.     

Comments on the derivation of the mixing angles

It is pointed out that Fritzsch's derivation of the mixing angles for a six-quark theory based on a SU(2)_L × SU(2)_R × U(1) model is in error. The correct formula for the mixing angles differs significantly from Fritzsch's results.     

A study of SU(3) × SU(2) × U(1) × U(1) as an intermediate energy subgroup of SO(10)

We analyze several patterns of symmetry breaking of SO(10) where SU(3)_c × SU(2) × U(1) × U(1) is an intermediate energy subgroup. Using constraints from the renormalization group and data from neutral-current experiments we show that if the only Higgs used in the low-energy breaking of the theory are those which can give mass to fermions then the possibility of a low intermediate mass scale is ruled out.     

The structure of weak interactions for composite quarks and leptons

We consider a model of quarks and leptons as quasi-Goldstone fermions which is based on an underlying supersymmetric SU(2)_HC × SU(2)′_HC preon theory. The spontaneous breakdown of a global U(6) × U(6)′ × U(1) symmetry to U(4) × U(4)′ × SU(2)_diag creates both quarks and leptons and at the same time allows for the possibility of having either residual or fundamental weak interactions. Effective lagrangians in the confining phase of the theory are compared to those emerging from a complementary picture and the problems connected with the nature of the weak interactions are discussed in this context also.     

Baryons in the effective lagrangian of strongly coupled lattice QCD

The effective action formulation of lattice QCD is extended to incorporate baryons. At strong coupling we find a generalized σ model where the baryons obtain their mass via a non-vanishing vacuum expectation value 〈¯ΦΦ〉. The SU(3) effective potential is worked out for Susskind fermions taking into account the influence of the baryons, and the results are compared with the U(3) theory. The large-N behavior of the SU(N) theory is studied as well. A loop expansion method is proposed for dealing with general multi-component baryon fields in both Susskind's and Wilson's fermion formulations.     

Unification of families based on a coset space E7/SU(5) × SU(3) × U(1)

We show that the usual three families of quarks and leptons are identifiable with quasi Nambu-Goldstone fermions in a supersymmetric non-linear realization of E₇ corresponding to the Kähler manifold E₇/SU(5) × SU(3) × U(1). So the triplication of families suggests the underlying preon theory realizing the global E₇ linearly. Possible connections with N = 8 supergravity are also discussed.     

Nonabelian electric and magnetic flux in unified SU(5) gauge theory

We study the long-distance behaviour of pure unified SU(5) gauge theory in the limit when the electroweak subgroup is unbroken. We show that the symmetry breaking pattern SU(5)→SU(3)_c×SU(2)×U(1)_Y, with SU(3)_c and SU(2) ×U(1)_Y realized, respectively, in confining and coulombic phases, is a possible dynamical phase of the SU(5) theory. The proof relies on showing that the duality equation of 't Hooft, relating the electric and magnetic flux, is exactly satisfied for the above symmetry breaking pattern. The infrared structure of SU(5), broken down to SU(3)_c×SU(2)×U(1)_Y, is not self-dual.     

Supersymmetric family unification

The superheavy symmetry breaking of the gauge group in supersymmetrized unified theories is studied. The requirement that supersymmetry be unbroken strongly constraints the possible gauge group breaking, and we systematize such constraints group theoretically.In model building, one issue is whether to permit an adjoint matter superfield with concomitant color exotic fermions. A second issue is that of naturalness which is complicated by the well-known supersymmetry non-renormalization theorems.Both with and without an adjoint matter superfield, the most promising group appears to be SU(9) where three families can be naturally accommodated, at least for low-energy gauge group SU(3)×SU(20×U(1). With an extra U(1) factor, as advocated by Fayet, the non-renormalization theorem must be exploited.     

Light composite fermions

't Hooft's conditions for massless composite fermions are discussed. We then study the various mechanisms through which such composite fermions can acquire a small mass. Two new mass generation mechanisms are proposed.     

Superunification from eleven dimensions

We show how N = 8 supersymmetry can break spontaneously to N = 1 at the Planck scale via a Kaluza-Klein compactification of d = 11 supergravity on the squashed seven-sphere. Features unique to Kaluza-Klein supergravity are (i) the massless gravitino of the N = 1 phase comes from a massiveN = 8 supermultiplet, (ii) the scalars developing nonzero VEVs also belong to massive N = 8 supermultiplets, (iii) parity remains unbroken when N = 8 breaks to N = 1.Next we ask whether the resulting N = 1 theory can provide a realistic SU(3) × SU(2) × U(1) unification and speculate that it might if some of the gauge bosons and fermions are composite as in the EGMZ model. In contrast to their model, however, we avoid unwanted helicities and problems with their non-compact E₇. Moreover, we suggest a scheme in which the electroweak SU(2) × U(1) is a subgroup of the d = 11 general coordinate group but that the strong SU(3) is a subgroup of the d = 11 local Lorentz group and are not, therefore, to be combined into a GUT. The special properties of the seven-sphere also suggest a possible solution of the cosmological constant problem involving fermion condensates.     

Hierarchical fermion masses in SU(5)

Rediative masses are generated for the first and the second fermion families by exploiting the idea that their chirality is a symmetry of the “low-energy” SU(3) × SU(2) × U(1) approximation of SU(5), broken only by including the effects of superheavy particles. With only 5's of Higgs coupled to fermions and getting a non-zero vacuum expectation value, we unavoidably get (i) $\text{m}{}_{\mathrm{<mtext>s</mtext>}}\text{=}\text{m}{}_{\mathrm{\mu }}\text{3}$ at the grand unification scale; (ii) the charm quark needing a direct mass as the third family; (iii) neutrino masses of size $\text{? (}\text{α}\text{π}\text{)}\text{M}{}_{\mathrm{W}}{}^2\text{M}$.     

Generations in the rishon model

We present a model for fermions composed of rishons in which colour plays a determinant role providing for only three generations. The couplings with the gauge bosons of the SU(2)_L × SU(2)_R × U(1)_B?L theory as well as with Higgs bosons are determined by the colour substructures. Two appealing possibilities emerge: the Cabibbo mixing angles could be small due to their dependence on the colour coupling constant and the fermionic mass hierarchy could be related to the fact that the products of higher representations have a richer decomposition allowing for the coupling with more Higgs fields.     

Adler-Bell-Jackiw anomaly and fermion-number breaking in the presence of a magnetic monopole

In (V - A) theories, fermion number is broken in the presence of the 't Hooft-Polyakov magnetic monopole through the Adler-Bell-Jackiw anomaly. An exactly solvable zeroth-order approximation for evaluating Green functions of zero-angular-momentum fermions in the presence of a monopole is developed in the case of an SU(2) model with massless left-handed fermions. Within this approximation the density of the fermion-number breaking condensate is calculated. This density is found to be O(1), i.e. to be independent of the coupling constant and of the vacuum expectation value of the Higgs field. The corrections to the approximation are estimated. It is argued that the above effect can give rise to the strong baryon-number breaking in monopole-fermion interactions in SU(5) grand unified theory.     

Spectral functions in the two-dimensional Hubbard model within a spin-charge rotating frame approach

We have performed electronic spectral function calculations for the Hubbard model on the square lattice using recently developed quantum SU(2) × U(1) rotor approach that enables a self-consistent treatment of the antiferromagnetic state. The collective variables for charge and spin are isolated in the form of the space-time fluctuating U(1) phase field and rotating spin quantization axis governed by the SU(2) symmetry, respectively. As a result interacting electrons appear as composite objects consisting of bare fermions with attached U(1) and SU(2) gauge fields. This allows us to write the fermion Green’s function in the space-time domain as a product of the SU(2) gauge fields, U(1) phase propagator and the pseudo-fermion correlation function. Consequently, the calculation of the spectral line shapes now reduces to performing the convolution of spin, charge and pseudo-fermion Green’s functions. The collective spin and charge fluctuations are governed by the effective actions that are derived from the Hubbard model for any value of the Coulomb interaction. The emergence of a sharp peak in the electron spectral function in the antiferromagnetic state indicates the decay of the electron into separate spin and charge carrying particle excitations.