T-matrix approach to quarkonium correlation functions in the quark-gluon plasma

Abstract

We study the evolution of heavy quarkonium states with temperature in a Quark Gluon Plasma (QGP) by evaluating the in-medium Q-Q T −matrix within a reduced Bethe-Salpeter equation in both S− and P −wave channels. The underlying interaction kernel is extracted from recent finite-temperature QCD lattice calculations of the singlet free energy of a Q-Q pair. The bound states are found to gradually move above the Q-Q threshold after which they rapidly dissolve in the hot system. The T −matrix approach is particularly suited to investigate these mechanisms as it provides a unified treatment of bound and scattering states including threshold effects and the transition to the (perturbative) continuum. We apply the T −matrix to calculate Q-Q spectral functions as well as pertinent Euclidean-time correlation functions which are compared to results from lattice QCD. A detailed analysis reveals large sensitivities to the interplay of bound and scattering states, to temperature dependent threshold energies and to the "reconstructed" correlator used for normalization. We furthermore investigate the impact of finite-width effects on the single-quark propagators in the QGP as estimated from recent applications of heavy-quark rescattering to RHIC data.

Dilepton radiation at the CERN super-proton synchrotron

“…In cold nuclear matter, the renormalization of the π-ρ cloud has been found to be rather sensitive to the medium effects on the ρ [38,48,53,54], which is due to the fact that the ω → πρ(→ πππ) decay proceeds via the low-mass tail of the ρ-spectral function below its nominal mass of 770 MeV. In Ref.…”

“…[33]), resulting in Γ ωP (̺ 0 ) ≃ 60 MeV. Likewise, a large contribution to second order in the nuclear density, O(̺ 2 N ), to Γ ωP (̺ N ) arises due to the simultaneous dressing of both π and ρ [54]. Following Ref.…”

Quarkonia in the deconfined phase: Effective potentials and lattice correlators

“…In potential model calculations, the reconstructed correlators have been usually considered at zero temperature [39,41,42], adding to the bound state contribution -calculated with a phenomenological confining potential -the perturbative QCD continuum. This choice obviously poses another problem of consistency (besides the one, already mentioned, of the consistency between the bound and the continuum spectra), since above T c one is using a lattice-derived potential and at T = 0 a phenomenological (fitted to the data) one.…”

“…Since the reliability of MEM to extract the spectral functions is not fully established yet, the check of consistency of the potential model has been mainly devoted to a direct comparison with the euclidean correlators in a number of papers [37,38,39,40,41,42].…”

Quantum mechanical model for J/ψ suppression in the LHC era

“…The description of quarkonia states in a hot QGP medium in the vicinity of the critical temperature should therefore treat bound and scattering states on an equal footing. This is appropriately achieved within a thermodynamical Tmatrix approach, which has been developed to address the spectral properties of quarkonia [23] as well as open flavor meson states [24,25,26]. It is also worth noting that inelastic collisions are responsible for absorption of J/ψ in a hadron gas of light π and ρ mesons since the corresponding cross sections can be sufficienly large [21,27,28,29,30].…”