Natural top quark condensation (a redux)

Abstract

The Nambu–Jona-Lasinio (NJL) model involves a pointlike 4-fermion interaction. While it gives a useful description of chiral dynamics (mainly in QCD), it nonetheless omits the crucially important internal wave-function of a two-body bound state, $\varphi \left(r\right)$. This becomes significant near critical coupling where $\varphi \left(r\right)$ extends to large distance, leading to dilution and suppression of induced couplings $\propto \varphi \left(0\right)$, such as the Yukawa and quartic couplings, as well as reduced fine-tuning of a hierarchy. In top quark condensation, where the Brout-Englert-Higgs (BEH) boson is a $\bar{t}t$ bound state and we have a UV completion such as topcolor, we must go beyond the NJL model and include effects of $\varphi \left(r\right)$. We provide a formulation of this for the BEH boson, and find that it leads to an extended $\varphi \left(r\right)$, a significantly reduced and natural composite scale of $M_0\sim 6$ TeV, a successful prediction for the quartic coupling, λ, and fine–tuning that is reduced to a few percent, providing a compelling candidate solution to the naturalness problem of the BEH boson. The theory is testable and the associated new physics may soon emerge at LHC energy scales.