The Fundamental-Weak 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: ∼ e 40 . Using renormali-sation group equations for the SM, we obtain the effective potential in the 2-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 2-loop approximation shows that, with initial values of the top Yukawa coupling in the interval h ( M t ) = 0 . 95 ± 0 . 03 (here M t is the top quark pole mass), a second minimum of the SM effective potential can exist in the region φ min 2 ≈ 10 16 − 10 22 GeV. A prediction is made of the existence of a new bound state of 6 top quarks and 6 anti-top quarks, formed due to Higgs boson exchanges between pairs of quarks/anti-quarks. 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.