Some Unfinished Thoughts on Strong Yukawa Couplings

Abstract

Yukawa couplings of electroweak Goldstone bosons can be inferred from experiment, but the existence of an elementary Higgs boson is not yet an established fact. If a sequential chiral quark generation does exist, it would bring us now into the strong Yukawa coupling regime. Guided by a Bethe--Salpeter equation approach, we postulate that the leading collapse state, the (heavy) isotriplet and color-singlet $\pi_1$ meson, becomes the Goldstone boson $G$ itself. Viewing it as a deeply bound state, a gap equation is constructed. This "`bootstrap" picture for electroweak symmetry breaking relies on strong Yukawa coupling, without providing any theory of the latter.