We examine the possibility that the physical spectrum of a vector-like gauge field theory exhibits an enhanced global symmetry near a chiral phase transition. A transition from the Goldstone phase to the symmetric phase is expected as the number of fermions N f is increased to some critical value.Various investigations have suggested that a parity-doubled spectrum develops as the critical value is approached. Using an effective Lagrangian as a guide, we note that parity doubling is associated with the appearance of an enhanced global symmetry in the spectrum of the theory. The enhanced symmetry would develop as the spectrum splits into two sectors, with the first exhibiting the usual pattern of a spontaneously broken chiral symmetry, and the second exhibiting an additional, unbroken symmetry and parity doubling.The first sector includes the Goldstone bosons and other states such as massive scalar partners. The second includes a parity-degenerate vector and axial vector along with other possible parity partners. We note that if such a nearcritical theory describes symmetry breaking in the electroweak theory, the additional symmetry suppresses the contribution of the parity doubled sector to the S parameter.

We show that in pure gauge QCD (or any pure non-Abelian gauge theory) the condition for the existence of a global minimum of energy with a gluon (gauge boson) mass scale also implies the existence of a fixed point of the β function. We argue that the frozen value of the coupling constant found in some solutions of the Schwinger-Dyson equations of QCD can be related to this fixed point. We also discuss how the inclusion of fermions modifies this property.

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 .

Motivated by the upcoming Higgs analyses, we investigate the importance of the complementarity of the Higgs boson chase on the low-mass weakly interacting massive particle (WIMP) search in direct detection experiments and the gamma-ray emission from the Galactic Center measured by the Fermi-LAT telescope in the context of the SUð3Þ c SUð3Þ L Uð1Þ N. We obtain the relic abundance, thermal cross section, and the WIMP-nucleon cross section in the low-mass regime and network them with the branching ratios (BRs) of the Higgs boson in the model. We conclude that the Higgs boson search has a profound connection to the dark matter problem in our model, in particular for the case that (M WIMP < 60 GeV) the BRðH ! 2 WIMPsÞ * 90%. This scenario could explain the gamma-ray emission from the Galactic Center observed by the Fermi-LAT telescope through the b " b channel with a WIMP in the mass range of 25-45 GeV, while still being consistent with the current limits from XENON100 and CDMSII. However, after the recent LHC measurements concerning the Higgs, this window has been completely forfended, implying that M WIMP > M H =2 and, consequently, ruling out any attempt to explain the Fermi-LAT observations, although still offering a region of the parameter space consistent with the current bounds. Lastly, we show that our model has a Standard Model-like Higgs boson for the regime that M WIMP > M H =2, by computing the BRs into bb, and .

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.