Gauge theory of Lorentz group as a source of the dynamical electroweak symmetry breaking

Abstract

We consider the gauge theory of Lorentz group coupled in a nonminimal way to fermions. We suggest the hypothesis that the given theory may exist in the phase with broken chiral symmetry and without confinement. The lattice discretization of the model is described. This unusual strongly coupled theory may appear to be the source of the dynamical electroweak symmetry breaking. Namely, in this theory all existing fermions interact with the SO(3, 1) gauge field. In the absence of the other interactions the chiral condensate may appear and all fermionic excitations may acquire equal masses. Small corrections to the gap equations due to the other interactions may cause the appearance of the observed hierarchy of masses.The scalar excitation recently found at 125 GeV is now interpreted as the Higgs boson [1,2]. The existence of the other Higgs bosons with the same (or, larger) production cross -sections is excluded within the wide ranges of masses approximately from 130 GeV to 550 GeV [3, 4]. However, this does not mean that the existence of scalar particles within these ranges of masses is excluded completely. The particles with smaller values of production cross -sections are allowed. In [5][6][7] it was suggested that such particles may appear. It was supposed that these particles together with the 125 GeV Higgs may be composed of known Standard Model fermions due to the unknown strong interaction between them (with the scale Λ above 1 TeV). This unknown interaction if it exists should have very specific properties that make it different from the conventional technicolor (TC) interactions [8-10] (for a recent alternative to the technicolor see, for example, [11]).First, these interactions cannot be confining since otherwise they would confine quarks and leptons to the extremely small regions of space ∼ 1/Λ, so that all strong and weak interaction physics would be missed. At the same time these interactions should provide the spontaneous chiral symmetry breaking needed to make W and Z bosons massive. Some models with such properties were already discussed in the framework of the topcolor [12, 17-21, 33, 35, 38]. For the review of the conventional technicolor see [22][23][24]38]. The topcolor assisted technicolor (combines both technicolor and topcolor ingredients) was considered in [25][26][27][28][29]. The models based on the extended color sector were considered in [30,31]. For the top -seesaw see [32]. In [5,6,11] the scenario was suggested according to which the chiral condensates appear corresponding to some of the Standard Model fermion fields (not necessarily of the top quark only). This pattern provides both masses for the W, Z bosons and for the fermionic particles.The considerations of [5][6][7] were based on the NJL approximation. Due to the non -renormalizability it is to be considered as the phenomenological model with the finite ultraviolet cutoff

Strong dynamics behind the formation of the 125 GeV Higgs boson

“…at the level of the hydrodynamics). It was suggested to apply the similar principles of stability to subtract divergences from the vacuum energy in the quantum theory in the presence of gravity [19] and to subtract quadratic divergences from the contributions to the Higgs boson masses in the NJL models of composite Higgs bosons [20][21][22][23]. Now we understand, that the zeta regularization allows to implement such principles of stability to various theories in a very natural and common way.…”

Schwinger–Dyson equation and NJL approximation in massive gauge theory with fermions

“…(45) is satisfied near to the criticality. The important feature of the NJL model that was not considered here is the Nambu sum rule [44,46,45,47] that relates the values of masses of scalar excitations with the value of dynamical fermion mass. In our case this sum rule gives for the Higgs boson M H = 2m.…”

Nambu sum rule in the NJL Models: from superfluidity to top quark condensation

“…(After the suitable rescaling Λ plays the role of the cutoff, while the eigenvalues of L, R, I are all close to 1.) The possible origin of this pattern was discussed in [30], where it is suggested that the given NJL model originates from the gauge theory of Lorentz group coupled in an equal way to all existing fermions. The basis of observed quarks corresponds to the diagonal form of L, R, I.…”