Hierarchy-Problem and a Bound State of 6 t and 6 $\bar{t}$

Abstract

We propose a unification of some fine-tuning problems -- really in this article only the problem of why the weak scale is so small in energy compared to a presumed fundamental scale, being say the Planck scale -- by postulating the zero or very small value of the cosmological constant not only for one but for several vacua. This postulate corresponds to what we have called the Multiple Point Principle, namely that there be many ``vacuum'' states with the same energy density. We further assume that 6 top quarks and 6 anti-top quarks can bind by Higgs exchange so strongly as to become tachyonic and form a condensate. This gives rise to the possibility of having a phase transition between vacua with and without such a condensate. The two vacua distinguished by such a condensate will have the same cosmological constant provided the top Yukawa coupling is about $1.1 \pm 0.2$, in good correspondence with the experimental value. The further requirement that this value of the Yukawa coupling, at the weak scale, be compatible with the existence of a third vacuum, with a Higgs field expectation value of the order of the fundamental scale, enforces a hierarchical scale ratio between the fundamental and weak scales of order $10^{16}$ -- $10^{20}$.