Real-time static potential in hot QCD

Abstract

We derive a static potential for a heavy quark-antiquark pair propagating in Minkowski time at finite temperature, by defining a suitable gauge-invariant Green's function and computing it to first non-trivial order in Hard Thermal Loop resummed perturbation theory. The resulting Debye-screened potential could be used in models that attempt to describe the "melting" of heavy quarkonium at high temperatures. We show, in particular, that the potential develops an imaginary part, implying that thermal effects generate a finite width for the quarkonium peak in the dilepton production rate. For quarkonium with a very heavy constituent mass M , the width can be ignored for T < ∼ g 2 M/12π, where g 2 is the strong gauge coupling; for a physical case like bottomonium, it could become important at temperatures as low as 250 MeV. Finally, we point out that the physics related to the finite width originates from the Landau-damping of low-frequency gauge fields, and could be studied non-perturbatively by making use of the classical approximation.

Melting of P wave bottomonium states in the quark-gluon plasma from lattice NRQCD

“…Here we mention that the applicability of nonrelativistic QCD (NRQCD) [16] on the lattice [17] to treat the b quark at finite temperature is motivated by the hierarchy of effective field theories formulated in Refs. [18][19][20][21]. We also emphasise that the use of NRQCD enhances the signature for quarkonium melting/survival, as it avoids several problems which have complicated the study of relativistic quarks in thermal equilibrium [22,23].…”

Mesonic screening masses at high temperature and finite density

“…The details can be found in [19]. Since the propagators (30), (31) as well as the couplings in Eq. (24) are diagonal in spin indices, and (σ i ) 2 = 1, the spin structure does not affect the result.…”

The relation between cross section, decay width and imaginary potential of heavy quarkonium in a quark–gluon plasma

“…This program for finite temperature T and zero chemical potential µ has been started in the last years [3,4]. Using these techniques the potential of [2] has been confirmed for T ≫ m D ∼ 1/r. The case 1/r ≫ T ≫ E ≫ m D was studied in [5] where corrections to decay width that can not be encoded in a potential were found.…”