Deciphering the minimum of energy of some walking technicolor models

Abstract

There are quasiconformal theories, like the minimal and ultraminimal technicolor models, which may break dynamically the gauge symmetry of the standard model and at the same time are compatible with electroweak precision data. The main characteristic of this type of models is their fermionic content in one or more higher dimensional representations; therefore it is not immediately known which model leads to the most attractive channel or the minimum vacuum energy state. We discuss the effective potential for composite operators for these models, verifying that their vacuum energy values are different, with the ultraminimal model having a deeper minimum of energy. DOI: 10.1103/PhysRevD.81.097702 PACS numbers: 12.60.Nz, 12.60.Fr The nature of the Higgs boson is one of the most important problems in particle physics, and there are many questions that may be answered in the near future by the LHC experiments, such as the following: Is the Higgs boson, if it exists at all, elementary or composite, and what are the symmetries behind the Higgs mechanism? The possibility that the Higgs boson is a composite state instead of an elementary one is more akin to the phenomenon of spontaneous symmetry breaking that originated from the effective Ginzburg-Landau Lagrangian, which can be derived from the microscopic BCS theory of superconductivity describing the electron-hole interaction (or the composite state in our case). This dynamical origin of the spontaneous symmetry breaking has been discussed with the use of many models, the technicolor (TC) model being the most popular one [1].Unfortunately we do not know the dynamics that form the scalar bound state, which should play the role of the Higgs boson in the standard model symmetry breaking. Most of the models for the spontaneous symmetry breaking of the standard model based on the composite Higgs boson system depend on specific assumptions about the dynamics responsible for the bound state formation [2], and the work in this area tries to find the TC dynamics dealing with the particle content of the theory, in order to obtain a technifermion self-energy that does not lead to phenomenological problems as in the scheme known as walking technicolor [3]. These are theories where the incompatibility with the experimental data has been solved, making the new strong interaction almost conformal and changing appreciably its dynamical behavior. We can obtain an almost conformal TC theory, when the fermions are in the fundamental representation, introducing a large number of TC fermions (n F ), leading to an almost zero function and flat asymptotic coupling constant. The cost of such a procedure may be a large S parameter [4] incompatible with the high precision electroweak measurements.TC models with fermions in other representations than the fundamental one, as happen in the minimal [5] (MWT) and ultraminimal [6] (UMT) TC models, are possible viable models without conflict with the known value for the measured S parameter, which may be calculated assuming valid the perturbative...

The extreme walking behavior in a 331-TC model

“…(1), μ ≈ 2 = 331 and 2 , it is not generated by the TC sector. In order to provide an example we consider the SU (2) T C case with the technifermionic content shown in [20], where n T F = 6. With this we obtain m φ 1 ∼ 124 GeV, m φ 2 ∼ 8.3 TeV, and 331 = 3 TeV and ET C ≈ 90 TeV.…”

“…[19,20] the gauge symmetry breaking in 3-3-1 models can be implemented dynamically because at the scale of a few TeVs the U (1) X coupling constant becomes strong. The exotic quark T introduced will form a condensate breaking SU (3) L ⊗ U (1) X to electroweak symmetry, in this paper we will numerically determine the U (1) X contribution to the dynamic mass of exotic quarks (T, S, D) and techniquarks (U , D ), which appear in the fermionic content of the model [20] following the same procedure as described in Ref. [19].…”

“…[19]. The Schwinger-Dyson equation for quarks (techniquarks) due to the U (1) X interaction can be written as [19,20] …”

“…In order to obtain the mass spectrum generated due to the U (1) X interaction, we follow the same procedure as described in Ref. [19] where the (Y i ) hypercharges of the exotic quarks (T, S, D) were assumed according to Table 1 and we include the corresponding hypercharges of the exotic techniquarks (U , D ) [20], which are singlets of SU (3) c .…”

Composite Higgs models, Technicolor and the muon anomalous magnetic moment

“…In particular, the model described in Ref. [10] the electroweak symmetry is broken dynamically by a technifermion condensate generated by the SU (2) T C Technicolor (TC) gauge group [11].…”