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

TL;DR

This paper reviews how mesons, as bound states of confined quarks, behave at zero and finite temperatures using Dyson--Schwinger equations, highlighting their properties, decays, and phase transitions in QCD.

Contribution

It applies a Poincaré-covariant Dyson--Schwinger framework with a specific kernel to study meson properties at finite temperature, including chiral restoration and deconfinement transitions.

Findings

Meson masses and decay constants are computed at zero and finite temperature.

Finite temperature results align with lattice QCD data.

The model prevents spurious quark-antiquark production effects.

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 Poincar\'e-covariant study of the masses and electroweak decay constants of the ground state pseudoscalars and vectors: $\pi$, $K$, $\rho/\omega$, $K^\star$ and $\phi$. Within the impulse approximation, we summarize results for the $\pi$ 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.