Perturbative corrections to technicolor

Abstract

The full solution of technicolor (TC) Schwinger-Dyson equations should include radiative corrections induced by extended technicolor (ETC) (or other) interactions. We verify that when TC is embedded into a larger theory including also QCD, these radiative corrections couple the different strongly interacting Schwinger-Dyson equations, providing a tiny mass to technifermions and changing the ultraviolet behavior of the gap equation solution. We argue about the origin of the different quark masses without appealing for different ETC boson masses, in one scenario where most of the new physics will appear in interactions with the third fermion generation and with a TC scalar boson possibly lighter than the TC characteristic scale (Λ TC ). DOI: 10.1103/PhysRevD.97.115035 The origin of fermion and gauge boson masses in the standard model (SM) of elementary particles is explained by their interaction with the Higgs boson. The discovery of this boson at the LHC [1,2] has crowned the SM; however, the data still cannot discard the possibility of this boson being a composite one. The case of a composite state, generating dynamical gauge symmetry breaking, instead of an elementary one, is more akin to the phenomenon of spontaneous symmetry breaking that originated from the Ginzburg-Landau Lagrangian. The latter can be derived from the microscopic Bardeen-cooper-schrieffer (BCS) theory of superconductivity describing the electron-hole interaction, which can be interpreted as a composite state. A similar mechanism happens in QCD where the chiral symmetry breaking is promoted by a nontrivial vacuum expectation value of a fermion bilinear operator and the Higgs role is played by the composite σ meson. In particular, the technicolor (TC) idea was the earliest attempt to build models in this direction [3,4].The main ideas about TC models were reviewed in Refs. [5,6] and recent phenomenological studies about this class of models can be seen in Refs. [7][8][9][10][11][12][13] and references therein. Despite the fact that TC models are much more complex than the ones with elementary scalar bosons, the main difficulty to build a realistic model lies in the ordinary behavior of the technifermion self-energy that is propor-where μ TC is the characteristic TC dynamical mass at zero momentum and γ the anomalous mass dimension. This self-energy leads to the known quark mass (m Q ) given by m Q ∝ μ 3 TC =M 2 E , where M E is the mass of an extended technicolor boson (ETC), which is a particle that may change flavors. In order to describe, for example, the top quark mass we need a small M E value, and this boson generates flavor changing neutral currents at one undesirable level.

Technicolor models with coupled systems of Schwinger-Dyson equations

“…With m F of order of several GeV and standard values for the condensate and technipion decay constant the technipion masses turn out to be of order of 100 GeV or higher, as discussed in Ref. [35]. Another way to see that technipion masses are enhanced through the calculation of a diagram that was already shown in Ref.…”

“…Another way to see that technipion masses are enhanced through the calculation of a diagram that was already shown in Ref. [35] (see Fig.4 of that reference). Any radiative boson exchange within a technipion modifying its mass will necessarily involve the technipion vertex connecting it to technifermions (Γ ΠF ).…”

“…In Ref. [35] we briefly proposed one specific TC model, which will be detailed here. As will be discussed at the end of this section, there is a large class of models that can be built along the same lines as the model described here.…”

“…In Ref. [35] we briefly commented that the technipion masses (m Π ) are enhanced in comparison with models where the TC self-energy does not have the form of Eq.(4). One of the arguments is quite simple: the technifermions obtain an effective mass (m F ) of several GeV through diagrams (a 3 ) and (a 4 ) of Fig.2.…”

“…The Takeuchi solution, when dominated by the four-fermion interaction, is not different from the behavior of the self-energy when a bare mass is introduced into the theory, or from irregular SDE solution [19]. Recently, we numerically solved the coupled TC [based on an SU (2) group] and QCD gap equations [35], which are depicted in the Fig.2. It turned out that both selfenergies have the same asymptotic behavior as Eq.…”