Can the symmetry breaking in the SM be determined by the "second minimum" of the Higgs potential?

Abstract

The possibility that the spontaneous symmetry breaking in the Standard Model (SM) may be generated by the Top-Higgs Yukawa interaction (which determines the so called ``second minimum" in the SM) is investigated. A former analysis about a QCD action only including the Yukawa interaction of a single quark with a scalar field is here extended. We repeat the calculation done in that study of the two loop effective action for the scalar field of the mentioned model. A correction of the former evaluation allowed to select a strong coupling $\alpha $($\mu,\Lambda_{QCD})=0.2254$ GeV at an intermediate scale $\mu=11.63$ GeV, in order to fix the minimum of the potential at a scalar mean field determining $175$ GeV for the single quark mass. Further, a scalar field mass $m=44$ GeV is evaluated, which is also of the order of the experimental Higgs mass. The work is also considering the effects of employing a running with momenta strong coupling. For this purpose, the finite part of the two loop potential contribution determined by the strong coupling, was represented as a momentum integral. Next, substituting in this integral the experimental values of the running coupling, the potential curve became very close to the one for constant coupling. This happened after simply assuming that the low momentum dependence of the coupling is "saturated" to a constant value being close to its lowest experimental value.