Heavy quarkonium dynamics at next-to-leading order in the binding energy over temperature

Abstract

Using the potential non-relativistic quantum chromodynamics (pNRQCD) effective field theory, we derive a Lindblad equation for the evolution of the heavy-quarkonium reduced density matrix that is accurate to next-to-leading order (NLO) in the ratio of the binding energy of the state to the temperature of the medium. The resulting NLO Lindblad equation can be used to more reliably describe heavy-quarkonium evolution in the quark-gluon plasma at low temperatures compared to the leading-order truncation. For phenomenological application, we numerically solve the resulting NLO Lindblad equation using the quantum trajectories algorithm. To achieve this, we map the solution of the three-dimensional Lindblad equation to the solution of an ensemble of one-dimensional Schrödinger evolutions with Monte-Carlo sampled quantum jumps. Averaging over the Monte-Carlo sampled quantum jumps, we obtain the solution to the NLO Lindblad equation without truncation in the angular momentum quantum number of the states considered. We also consider the evolution of the system using only the complex effective Hamiltonian without stochastic jumps and find that this provides a reliable approximation for the ground state survival probability at LO and NLO. Finally, we make comparisons with our prior leading-order pNRQCD results and experimental data available from the ATLAS, ALICE, and CMS collaborations.

Simulation of Lindblad equations for quarkonium in the quark-gluon plasma

“…The dipole approximation is found to be quantitatively useful for a short but long enough time for the relativistic heavy-ion collisions. This supports the application of such Lindblad equation to the phenomenological studies of quarkonium evolution as is done in [31][32][33], which is practically beneficial because the numerical cost is much less.…”

“…This is due to the mismatch between the periodic boundary condition and the linear approximation of the Lindblad operators C n ∝ x. In a short enough time and a large enough volume, our analysis supports the nontrivial utility of the quarkonium Lindblad equation in the dipole limit, whose full-scale simulation has just started for the relativistic heavy-ion collision experiments [31][32][33].…”

“…Description of quarkonium as an open quantum system [6,7] was motivated by the discovery of the in-medium complex potential [8][9][10][11]. Since then, it has been pioneered by [12][13][14][15][16][17][18] and further developed to the present form -the Lindblad equations [19,20] in several regimes, which are now available [21][22][23][24] and can be simulated [25][26][27][28][29][30][31][32][33][34][35] (see also [36][37][38] for reviews). In contrast to the hydrodynamics, quarkonium acts as a slow dynamical probe that locally couples to gluons.…”

Heavy quark momentum diffusion coefficient in 3D gluon plasma

“…It would be interesting to study the phenomenological implications of these results in more detail. One exciting perspective is to include them into the quantum trajectories framework [6,45] to study the impact of initial stages on quarkonium dynamics via κ i (τ ). It is also possible to address the evolution of other transport coefficients during the initial non-equilibrium dynamics: in a separate paper we use the EKT setup to calculate the evolution of the jet quanching parameter q.…”