Light composite Higgs from an effective action for technicolor

Abstract

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 self-energy that depends on a certain parameter ($\ensuremath{\alpha}$), 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, (${M}_{H}\ensuremath{\le}\mathcal{O}(700)\text{ }\text{ }\mathrm{GeV}$ for $SU(2{)}_{\mathrm{TC}}$), and the experimental data on the Higgs boson mass constrain $SU(N{)}_{\mathrm{TC}}$ technicolor gauge groups to be smaller than $SU(10{)}_{\mathrm{TC}}$.