A New-Old Approach to Composite Scalars with Chiral Fermion Constituents

TL;DR

This paper develops a Lorentz-invariant theory of composite scalars made of chiral fermions, incorporating a non-pointlike internal structure, and explores its implications for spontaneous symmetry breaking and hierarchy fine-tuning.

Contribution

It introduces a novel formalism that extends the NJL model by including a spatially extended wave-function for bound states, reducing fine-tuning in hierarchy problems.

Findings

Bound states exhibit a non-pointlike internal wave-function.

Power-law suppression of induced couplings reduces fine-tuning.

Potential for realistic top-condensation models.

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, $\phi(r)$, which satisfies a Schr\"odinger-Klein-Gordon (SKG) equation with eigenvalue $\mu^2$. For super-critical coupling, $g_0 >g_{0c}$, we have $\mu^2< 0$ leading to spontaneous symmetry breaking. The binding of chiral fermions is semiclassical, and 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, $\phi(r)$, remains spatially extended and dilutes $\phi(0)$. 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.