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 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.
Highlights
The so called “second minimum” of the Higgs field potential in the Standard Model is the result of the Yukawa interaction of the Higgs field with the Top quark
The idea was to evaluate the two loop effective potential for the scalar field, which in the Standard Model (SM) is responsible for the generation of the “second minimum” and to study the possibility of choosing the renormalization conditions to fix the value of the single fermion mass as equal to the top quark one 175 GeV
Since the addition of a positive mass squared term is a natural choice for the starting Lagrangian, the model allows to conclude that the consideration of the “second minimum” to generate the spontaneous symmetry breaking in the modified SM to be considered, opens the possibility of fixing the observed value of the Higgs mass
Summary
The so called “second minimum” of the Higgs field potential in the Standard Model is the result of the Yukawa interaction of the Higgs field with the Top quark. This result indicates that the diminishing of the coupling with momentum does not drastically alter the behavior of the effective potential, which can be fixed to retain a minimum at a scalar field mean value imposing a Top quark mass of 175 GeV Another outcome, is that the new evaluation for the effective potential at constant coupling shows a second derivative at its minimum which predicts a scalar field mass of nearly m = 44 GeV. This result is smaller but yet close to the observed.
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