The fundamental-electroweak scale hierarchy in the standard model

The multiple-point principle, according to which several vacuum states with the same energy density exist, is put forward as a fine-tuning mechanism predicting the ratio between the fundamental and electroweak scales in the Standard Model (SM). It is shown that this ratio is exponentially huge: ∼e40. Using renormalization group equations for the SM, we obtain the effective potential in the two-loop approximation and investigate the existence of its postulated second minimum at the fundamental scale. The investigation of the evolution of the top-quark Yukawa coupling constant in the two-loop approximation shows that, with initial values of the top-quark Yukawa coupling in the interval h(Mt)=0.95±0.03 (here, Mt is the top-quark pole mass), a second minimum of the SM effective potential can exist in the region φmin2∼1016-1022 GeV. A prediction is made of the existence of a new bound state of six top quarks and six antitop quarks, formed owing to Higgs boson exchanges between pairs of quarks-antiquarks. This bound state is supposed to condense in a new phase of the SM vacuum. This gives rise to the possibility of having a phase transition between vacua with and without such a condensate. The existence of three vacuum states (new, electroweak, and fundamental) solves the hierarchy problem in the SM