We compute an effective action for a composite Higgs boson formed by new fermions belonging to a general technicolor non-Abelian gauge theory, using a quite general expression for the fermionic selfenergy that depends on a certain parameter ( ), that defines the technicolor theory from the extreme walking behavior up to the one with a standard operator product expansion behavior. We discuss the values of the trilinear and quadrilinear scalar couplings. Our calculation spans all the possible physical possibilities for mass and couplings of the composite system. In the case of extreme walking technicolor theories we verify that it is possible to have a composite Higgs boson with a mass as light as the present experimental limit, contrary to the usual expectation of a heavy mass for the composite Higgs boson. In this case we obtain an upper limit for the Higgs boson mass, (M H Oð700Þ GeV for SUð2Þ TC ), and the experimental data on the Higgs boson mass constrain SUðNÞ TC technicolor gauge groups to be smaller than SUð10Þ TC .

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.

We study chiral symmetry breaking in QCD-like gauge theories introducing a confining effective propagator, as proposed recently by Cornwall, and considering the effect of dynamical gauge boson mass generation. The effective confining propagator has the form 1/(k 2 + m 2 ) 2 and we study the bifurcation equation finding limits on the parameter m below which a satisfactory fermion mass solution is generated. Considering the evidences that the coupling constant and the gauge boson propagator are damped in the infrared, due to the presence of dynamically massive gauge bosons, the major part of the chiral breaking is mostly due to the confining propagator. We study the asymptotic behavior of the gap equation containing confinement and massive gauge boson exchange, and find that the symmetry breaking can be approximated at some extent by an effective four-fermion interaction generated by the confining propagator. We compute some QCD chiral parameters as a function of m, finding values compatible with the experimental data. Within this approach we expect that lattice simulations should not see large differences between the confinement and chiral symmetry breaking scales independent of the fermionic representation and we find a simple approximate relation between the fermion condensate and dynamical mass for a given representation as a function of the parameters appearing in the effective confining propagator.

Scalar composite boson masses have been computed in QCD and technicolor theories with the help of the homogeneous Bethe-Salpeter equation, resulting in a scalar mass that is twice the dynamically generated fermion or technifermion mass (m dyn ). We show that in the case of walking (or quasiconformal) technicolor theories, where the m dyn behavior with the momenta may be quite different from the one predicted by the standard operator product expansion, this result is incomplete and we must consider the effect of the normalization condition of the Bethe-Salpeter equation to determine the scalar masses. We compute the composite Higgs boson mass for several groups with technifermions in the fundamental and higher dimensional representations and comment about the experimental constraints on these theories, which indicate that models based on walking theories with fermions in the fundamental representation may, within the limitations of our approach, have masses quite near the actual direct exclusion limit.