Mesons as Bound States of Confined Quarks: Zero and Finite Temperature

Abstract

We survey recent work on the properties and decays of mesons as bound states of confined quarks at both zero and finite temperature. The framework for these investigations is the set of QCD Dyson--Schwinger equations truncated to ladder-rainbow level. The infrared structure of the ladder-rainbow kernel is described by two parameters; the ultraviolet behavior is fixed by the one-loop renormalizaton group behavior of QCD. The work is restricted to the $u$, $d$ and $s$ quark sector and allows a Poincaré-covariant study of the masses and electroweak decay constants of the ground state pseudoscalars and vectors: $π$, $K$, $ρ/ω$, $K^\star$ and $ϕ$. Within the impulse approximation, we summarize results for the $π$ and $K$ charge form factors. Their timelike behavior exhibits the vector meson production resonances and from this the associated vector meson strong decay constants are extracted. The confining property of the quark self-energy dynamically produced in this work prevents the appearance of spurious $\bar{q}q$ production effects. The finite temperature behavior of this model, and closely related ones, is summarized for: the chiral restoration transition, the deconfinement transition, the $T$-dependence of the spatial meson mode masses, and the $T$-dependence of selected electroweak and strong decay widths. The $T$-dependence obtained for meson masses is compared to results from lattice QCD.