Spectroscopy, Scaling and Critical Indices in Strongly Coupled Quenched QED

Abstract

The interplay of spectroscopy, scaling laws and critical indices is studied in strongly coupled quenched QED. Interpreted as a model of technicolor having strong interactions at short distances, we predict the techni-meson mass spectrum in a simplified model of a dynamically generated top quark mass $M_f$. Our results support the strict inequality that the techni-sigma mass $M_\sigma$ is less than twice the dynamical quark mass $M_f$, and confirm that the techni-pion is a Nambu-Goldstone boson. The level ordering $0 = M_\pi < M_\sigma < 2M_f < M_\rho < M_{a1} $ is found.An equation of state, and scaling laws are derived for the techni-meson masses by exploiting correlation length scaling. The resulting universality relations are confirmed by simulations on $16^4$, $32\times 16^3$ and $32^4$ lattices. The anomalous dimension $\eta$ is measured to be approximatively $0.50$ in good agreement with past lattice simulations and hyperscaling relations, as well as with the analytic solution of the quenched, planar gauged Nambu-Jona Lasinio model solved by continuum Schwinger-Dyson equation techniques.