Existence of mesons after deconfinement

Details Existence of mesons after deconfinement Existence of mesons after deconfinement

2007-06-27

arxiv.org/abs/0706.4012v2

Phys. Rev. C 76, 065212 (2007)

Physics

High Energy Physics

High Energy Physics - Phenomenology

14 pages, 3 figures; only the case T>T_c is discussed in v2

Scientific paper

10.1103/PhysRevC.76.065212

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.

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