A new-old approach to composite scalars with chiral fermion constituents

Abstract

We develop a dynamical, Lorentz invariant theory of composite scalars in configuration space consisting of chiral fermions, interacting by the perturbative exchange of a massive “gluon” of coupling g0 and mass M02 (the coloron model). The formalism is inspired by, but goes beyond, old ideas of Yukawa and the Nambu-Jona-Lasinio (NJL) model. It yields a non-pointlike internal wave-function of the bound state, ϕ(r), which satisfies a Schrödinger-Klein-Gordon (SKG) equation with eigenvalue μ2. For super-critical coupling, g02>g0c2, we have μ2<0 leading to spontaneous symmetry breaking. The binding of chiral fermions is semiclassical, not loop-level as in NJL. The mass scale is determined by the interaction as in NJL. We mainly focus on the short-distance, large M02 limit, yielding an NJL pointlike interaction, but the bound state internal wave-function, ϕ(r→), remains spatially extended and dilutes ϕ(0). This leads to power-law suppression of the induced Yukawa and quartic couplings and requires radically less fine-tuning of a hierarchy than does the NJL model. We include a discussion of loop corrections of the theory. A realistic top condensation model appears possible.