At present, in elementary particle physics a very interesting situation has arisen. It is related to the situation that we had at the beginning of the twentieth century before the discovery of quantum mechanics and the special theory of relativity. During the last decade many impressive experimental achievements have been done: top-quark discovery, measurement of the direct CP violation in the K-meson system as well as the CP violation in the Bmeson system, evidence of accelerated universe expansion, determination of portions of dark matter and dark energy in the universe, the establishment of relict radiation anisotropy, and so on. These results strengthen the status of the standard model (SM) as the model which successfully describes nature. However, we again see some small clouds in the clear sky of the SM-the experimental facts that have not found satisfactory explanations within the SM. This is first of all a neutrino mass smallness, an observation of solar and atmospheric neutrino oscillations, the value of the muon AMM, and the prediction of an equal amount of matter and antimatter in the universe. Moreover, experiments showed that the density of matter entering the SM constitutes approximately 5% of the matter density in the universe. From a theoretical point of view, the SM is also far from perfection because it leaves without answering many fundamental questions associated with its structure. The SM may be divided into three sectors: a gauge sector, a flavor sector, and a sector in which a gauge symmetry is breaking. Whereas the two first sectors have been studied in accelerating experiments (LEP at CERN, SLD∗ and BABAR† at SLAC, BELLE at KEK (Japan), and so on), now the sector of the spontaneous symmetry breaking attracts rapt attention, and not only because physicists hope to discover the Higgs boson at LHC, but because this sector can give the first hints on the existence of New Physics beyond the SM. The Higgs mechanism in the SM represents only the description of the electroweak symmetry breaking. It does not give any explanations of the symmetry violation. In particular, dynamics that could explain the reason of the Higgs potential instability appearance at zero is absent. Consequently, the standard Higgs mechanism calls in question the contemporary understanding of the SM at

Particle and

the quantum level. There is a need to introduce additional structures (new particles, new symmetries, additional dimensions, and so on) in order to stabilize the electroweak scale. All this stimulates searches and investigations of models that lead to the same results like the SM in the low-energy region, while in the high-energy region their predictions are different from the SM predictions. There are at least three principle ways for the SM extension. The first consists in the building of models with a composite Higgs boson and a dynamical symmetry breaking. Nonobservation of the Higgs boson the SM predicts generates a class of Higgsless models. The third direction involves the Higgs mechanism and is based on the idea that the SM is considered as a low-energy approximation of some grand unification theory (GUT). For a symmetry group of the GUT, SO(10)−, E6-groups, and higher dimensionality groups that lead either to the extension of the electroweak group by factors SU(2) [88] and U(1) (see, for review, [59]) or to the replacement SU(2)L by SU(3)L (see, for example, [60]) may be employed. In this section we briefly discuss the first two classes of models. An abundance of elementary particles gives impetus to the assumption of a new level of

matter structure-quarks, leptons, and gauge bosons may be built from even smaller particles named preons.∗ Preons must be coupled by a superstrong interaction of a new type that should lead to the formation of quarks, leptons, and so on from preons. Such a hypothetical interaction has different names: hypercolor, technicolor, and the like. The interest peak to preon (or composite) models had fallen in the 1980s. Interest distinctly dropped because many of these models conflicted with the experimental data obtained at accelerators. Besides, after the first superstring revolution many physicist-theorists were inclined to the fact that the superstring theory is more logical and very promising. Accordingly, they focused their efforts in this direction. In the last few years, however, optimism concerning the superstring theory has waned, resulting in a regenerating of interest in composite models. Models of an extended technicolor are typical representatives of models with a composite

Higgs boson. The basic idea consists in the fact that preons (they are called technifermions here) are coupled by gauge interactions built by an analogy with QCD [61, 62]. At that, the existence of a set of new gauge charges, the technicolors, is postulated. The goal is to have a spontaneous symmetry breaking (SSB) theory with gauge interactions alone: there is no elementary scalar with its self-couplings and Yukawa couplings. The notion of a composite Higgs scalar is really not a new one. The idea of the Higgs phenomena was first suggested by the theory of superconductivity. There the electromagnetic gauge symmetry is spontaneously broken by the condensate (i.e., nonvanishing ground-state expectation value) of the electron pairs, which acts as an effective composite Higgs scalar. Thus, the SSB is brought on dynamically through the interactions of the electrons with the lattice phonons. One naturally wonders whether the QCD strong force that binds the colored quarks can be the interaction responsible for the SSB in the electroweak interaction? It turns out that such is not the case. However, the analysis of the way it fails suggests possible candidate theories. Let us consider the standard SU(3)c×SU(2)L×U(1)Y model and, for simplicity, restrict

ourselves to one generation of fermions. The Lagrangian is given by the expression:

L = −1 4 GaµνGaµν −

4 W iµνW iµν −

4 BµνBµν + i(qγµD

µq + lγµD µl). (13.1)

As there is no Higgs vacuum expectation value (VEV) to break the SU(2)L×U(1)Y gauge symmetry, it would seem that all fermions and all gauge bosons, including W± and Z, will remain massless. We shall see, this is actually not the case.