TL;DR: In this article, a third scenario called "oblique hypercolor" is proposed, in which a hyperquark condensate is formed which, although kinematically allowed to point in an SU(2) × U(1) preserving direction, is forced by the Yukawa interactions of the hyperquarks to misalign by a small angle, breaking SU( 2 + u(1).
TL;DR: In this paper, the distinction between different generations of quarks and leptons is given by the X -number, which does not lead to massless Goldstone bosons or to new anomalies and is already contained in the theory.
TL;DR: In this article, the strong dynamics associated with a composite Higgs model that simultaneously produces dynamical axions and solves the strong CP problem were considered, without introducing new elementary scalar fields, while also extending the range of axion masses that can be detected at collider experiments.
Abstract: We consider the strong dynamics associated with a composite Higgs model that simultaneously produces dynamical axions and solves the strong CP problem. The strong dynamics arises from a new Sp or SU(4) hypercolor gauge group containing QCD colored hyperfermions that confines at a high scale. The hypercolor global symmetry is weakly gauged by the Standard Model electroweak gauge group and an enlarged color group, SU(N + 3) × SU(N)′. When hyperfermion condensates form, they not only lead to an SU(5)/SO(5) composite Higgs model but also spontaneously break the enlarged color group to SU(3)c × SU(N)D. At lower energies, the SU(N)D group confines, producing two dynamical axions that eliminates all CP violation. Furthermore, small instantons from the SU(N)′ group can enhance the axion mass, giving rise to TeV scale axion masses that can be detected at collider experiments. Our model provides a way to unify the composite Higgs with dynamical axions, without introducing new elementary scalar fields, while also extending the range of axion masses that addresses the strong CP problem.
TL;DR: In this article, a model of massless composite quarks and leptons is proposed on the basis of the following requirements: 1) Confining hypercolor gauge forces which are asymptotically free with a scale Λ H in the TeV range.
TL;DR: In this article, the authors explore the extent to which string theories with higher-level gauge symmetries and nonstandard hypercharge normalizations can reconcile the discrepancy between the string unification scale and the GUT scale extrapolated from the MSSM.