Light composite vector bosons.

In gauge theories with slowly-running coupling constants, it may be possible for four-fermion operators to be nearly marginal. Such operators can possess asymptotically weak couplings, and can plausibly give rise to light composite vector mesons. † On leave from the Centre d’Etudes de Saclay, F-91191 Gif-sur-Yvette cedex, France CERN-TH.6767/92 December, 1992 The so-called Standard Model of accessible-energy particle physics, in spite of its increasingly precise experimental confirmation, remains unsatisfactory for several theoretical reasons. One of these is the hierarchy problem: it is unnatural for the Higgs scalar to appear in the theory at all, since its mass is not protected by any symmetry. Another is the replication of flavors and associated mass and mixing-angle parameters: these may be technically natural, but are puzzling nonetheless. These theoretical defects have prompted the development of many extensions to the Standard Model over the past two decades. Sensible extensions should possess a limit in which they reduce to the Standard Model, as this allows them to explain why the latter is such a successful effective theory at currently accessible energies. Such extensions can solve the hierarchy problem: both supersymmetry and technicolor [1] models (with or without grand unification) do. The former protects a fine-tuning, while the latter also explains the origin of a small scale (compared to the other known scale, the Planck scale). The flavor problem, on the other hand, is evidently quite hard: supersymmetric models do not even address it, while the literature is littered with the corpses of extensions to technicolor models that have succumbed either to the presence of excessive flavor-changing neutral currents or to the inadmissibility of a heavy top-quark, or to both. Both of these approaches presume that the flavor physics underlying the Standard Model can be explained purely in terms of weak-coupling physics, possibly supplemented by a scaled-up version of QCD. This is not necessarily wrong, but does seem a bit presumptuous, especially in light of the growing evidence that one of the parameters (the top Yukawa coupling) may be large enough to produce non-trivial dynamics. It thus seems sensible to search for other extensions to the Standard Model in which strong-coupling dynamics plays a role. One step in this direction was taken by Bardeen, Hill, and Lindner (BHL) [2], following earlier work [3]. They introduced a Nambu–Jona-Lasinio–type [4] four-fermion coupling of the top quark with a large dynamically-generated anomalous dimension; at lower energies, it becomes strong, generating an SU(2)×U(1)-breaking condensate, along with a composite Higgs scalar. In the limit originally considered by these authors, their model was later shown to be completely equivalent to the Standard Model [5]. Far from being a defect, this is in fact a virtue, as explained above. Interesting extensions may be obtained not by taking the BHL ‘cutoff’ (in their language) very high, but rather in taking it as low as possible without violating known experimental constraints [6]. In this letter, I explore another possible avenue for generating extensions to the Standard Model: rather than rewriting the Yukawa interaction in terms of four-fermion couplings, and generating a composite scalar, I rewrite the spontaneously-broken gauge interactions in terms of four-