Naturally Self-Tuned Low Mass Composite Scalars

Abstract

Scalar bosons composed of a pair of chiral fermions in a non-confining potential have an effective Yukawa coupling, $g$, to free external chiral fermions. At large distance a Feynman loop of external fermions generates a scale invariant potential, $V_{loop}\propto -g^2/r^2$, which acts on valence fermions for separation $\rho =2r$. This generally forces the $s$-wave ground state to deform to a static, zero mass, configuration, and for slowly running, perturbative $g$, a large external "shroud" wave-function forms. This is related to old results of Landau and Lifshitz in quantum mechanics. The massless composite scalar boson ground state is then an extended object. Infra-red effects can generate a small mass for the system. This points to a perturbative BEH-boson composed of top and anti-top quarks and a novel dynamical mechanism for spontaneous electroweak symmetry breaking.

Comments: 16 pages, 4 figures; we correct a normalization error and establish the equivalence of the critical coupling in the NJL model with that of the Landau-Lifshitz solutions; several other corrections, elaborations and tweaks