Natural Top Quark Condensation (a Redux)

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, φ(r). This becomes significant near critical coupling where φ(r) extends to large distance, leading to dilution and suppression of induced couplings ∝ φ(0), such as the Yukawa and quartic couplings, as well as reduced fine-tuning of a hierarchy. In top quark condensation, where the BEH boson is a t̄t bound state and we have a UV completion such as topcolor, we must go beyond the NJL model and include effects of φ(r). We provide a formulation of this for the Brout-Englert-Higgs boson, and find that it leads to an extended φ(r), a significantly reduced and natural composite scale of M₀ ~ 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 new physics should begin to emerge on the multi-TeV mass scales and possibly accessible to the LHC.