Transport coefficients from in-medium quarkonium dynamics

Abstract

The in medium dynamics of heavy particles are governed by transport coefficients. The heavy quark momentum diffusion coefficient, κ, is an object of special interest in the literature, but one which has proven notoriously difficult to estimate, despite the fact that it has been computed by weak-coupling methods at next-to-leading order accuracy, and by lattice simulations of the pure SU(3) gauge theory. Another coefficient, γ, has been recently identified. It can be understood as the dispersive counterpart of κ. Little is known about γ. Both κ and γ are, however, of foremost importance in heavy quarkonium physics as they entirely determine the in and out of equilibrium dynamics of quarkonium in a medium, if the evolution of the density matrix is Markovian, and the motion, quantum Brownian; the medium could be a strongly or weakly coupled plasma. In this paper, using the relation between κ, γ and the quarkonium in medium width and mass shift respectively, we evaluate the two coefficients from existing 2+1 flavor lattice QCD data. The resulting range for κ is consistent with earlier determinations, the one for γ is the first non-perturbative determination of this quantity.

Quantum Brownian motion of a heavy quark pair in the quark-gluon plasma

“…This question of the evolution of a small quantum system "S" coupled to an environment "E" has been studied in detail in condensed matter physics. In that context the open-quantum-system approach has been developed and applied to the description of quarkonium in the QGP as well [34][35][36][37][38][39][40][41][42][43][44][45][46][47][48]. The ultimate goal then is to eventually simulate a quarkonium as an open quantum system in the QGP and extract information on the in-medium forces from experimental data of Υ and J/ψ measured at the LHC and RHIC [2,3,[49][50][51][52][53][54][55][56][57].…”

Holographic vector mesons in a dilaton background

“…Our set-up does not resolve that issue on a firm basis, since the thermal mass shifts of J/ψ and Υ in Fig. 3 are noticeably larger than the lattice QCD-based values quoted in [8]. In addition, the sign of the thermal mass shift can depend on the actual parameters a and b in the model Eq.…”

“…3. Such thermal mass shifts are employed in [8] to pin down the heavy-quark (HQ) transport coefficient γ which can be considered as the dispersive counterpart of the HQ momentum diffusion coefficient κ = 2T 3 /(DT ), where D stands for the HQ spatial diffusion coefficient. Reference [20] stresses the tension within previous holographic results [50], where positive mass shifts are reported, in contrast to negative shifts, e.g.…”

“…Since heavy quarks emerge essentially in early, hard processes, they witness the course of a heavy-ion collision -either as individual entities or subjects of dissociating and regenerating bound states [2,3,4]. Accordingly, the heavy-quark physics addresses such issues as charm (c,c) and bottom (b,b) dynamics related to transport coefficients [5,6,7,8,9] in the rapidly evolving and highly anisotropic ambient quark-gluon medium [10,11] as well as cc / bb states as open quantum systems [12,13,14,15]. The rich body of experimental data from LHC, and also from RHIC, enabled a tremendous refinement of our theoretical treatment which grew up on initiating ideas like "Mott mechanism and the hadronic to quark matter matter phase transition" [16], "J/ψ suppression by quark-gluon plasma formation" [17], "Dissociation kinetics and momentum dependent J/ψ suppression" [18], and "Statistical hadronization of charm in heavy ion collisions at SPS, RHIC and LHC" [19].…”

Quarkonium Production in the QGP

“…The last term assures that the master equation for ρ QQ preserves the positivity of its eigenvalues. (For other recent studies of the open-quantum systems approach for quarkonium, see [33][34][35][36][37]. )…”