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 $g_0$ and mass $M_0^2$ (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, $\varphi \left(r\right)$, which satisfies a Schrödinger-Klein-Gordon (SKG) equation with eigenvalue ${\mu }^2$. For super-critical coupling, $g_0^2>g_{0c}^2$, we have ${\mu }^2<0$ 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 $M_0^2$ limit, yielding an NJL pointlike interaction, but the bound state internal wave-function, $\varphi \left(\overrightarrow{r}\right)$, remains spatially extended and dilutes $\varphi \left(0\right)$. 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.