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

TL;DR

This paper investigates whether the symmetry breaking in the Standard Model can be explained by the second minimum of the Higgs potential, focusing on the role of the Top-Higgs Yukawa interaction and the effects of running couplings.

Contribution

It extends previous analyses by calculating the two-loop effective potential with a fixed and running strong coupling, exploring the conditions for the second minimum to match observed particle masses.

Findings

The effective potential's minimum can be aligned with the top quark mass at 175 GeV.

A scalar mass around 44 GeV is obtained, comparable to the Higgs mass.

The potential shape remains similar when incorporating the running coupling, assuming low-momentum saturation.

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 examined. A former analysis is extended about a QCD action only including the Yukawa interaction of a single quark with a scalar field. We repeat the calculation of the two loop effective action of the model for the scalar field. A correction of the evaluation allowed choosing 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 field determining $175$ GeV for the quark mass. A scalar field mass $m=44$ GeV is following, which is of the order than the experimental Higgs mass. The effects of considering a running with momenta coupling are studied. For this, 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 similar 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.