Hierarchy Problem and a new Bound State ∗

Instead of solving fine-tuning problems by some automatic method or by cancelling the quadratic divergencies in the hierarchy problem by a symmetry (such as SUSY), we rather propose to look for a unification of the different fine-tuning problems. Our unified fine-tuning postulate is the so-called Multiple Point Principle, according to which there exist many vacuum states with approximately the same energy density (i.e. zero cosmological constant). Our main point here is to suggest a scenario, using only the pure Standard Model, in which an exponentially large ratio of the electroweak scale to the Planck scale results. This huge scale ratio occurs due to the required degeneracy of three suggested vacuum states. The scenario is built on the hypothesis that a bound state formed from 6 top quarks and 6 anti-top quarks, held together mainly by Higgs particle exchange, is so strongly bound that it can become tachyonic and condense in one of the three suggested vacua. If we live in this vacuum, the new bound state would be seen via its mixing with the Higgs particle. It would have essentially the same decay branching ratios as a Higgs particle of the same mass, but the total lifetime and production rate would deviate from those of a genuine Higgs particle. Possible effects on the ρ parameter are