Existence of mesons after deconfinement

TL;DR

This paper analyzes the conditions under which mesons, specifically quark-antiquark pairs, can exist as bound states above the deconfinement temperature, using different potential models and their implications.

Contribution

It provides analytical criteria for meson existence above deconfinement by comparing free energy and internal energy potentials in a Schrödinger framework.

Findings

Only 1S bottomonium can be bound above T_c with free energy potential.

No bound states exist in the deconfined phase when using internal energy.

Quasi-bound states may exist at higher temperatures due to potential barriers.

Abstract

We investigate the possibility for a quark-antiquark pair to form a bound state at temperatures higher than the critical one ($T>T_c$), thus after deconfinement. Our main goal is to find analytical criteria constraining the existence of such mesons. Our formalism relies on a Schr\"{o}dinger equation for which we study the physical consequences of both using the free energy and the internal energy as potential term, assuming a widely accepted temperature-dependent Yukawa form for the free energy and a recently proposed nonperturbative form for the screening mass. We show that using the free energy only allows for the 1S bottomonium to be bound above $T_c$, with a dissociation temperature around $1.5\times T_c$. The situation is very different with the internal energy, where we show that no bound states at all can exist in the deconfined phase. But, in this last case, quasi-bound states could be present at higher temperatures because of a positive barrier appearing in the potential.