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.

Non-equilibrium evolution of quarkonium in medium in the open quantum system approach

“…Using such a strategy, in Ref. [35] we derived a GKSL equation that is accurate to order E/T and respects positivity. 1 This allows one to map the quantum master equation to a GKSL equation that can be solved using a stochastic unraveling called the quantum trajectories algorithm [35,61].…”

“…In Refs. [35,37] it was found that the NLO OQS+pNRQCD framework provided a good description of existing experimental data from the ALICE, ATLAS, and CMS collaborations for both the nuclear modification factor, R AA , and elliptic flow, v 2 .…”

“…In recent years resummed perturbative and effective field theory calculations of the imaginary part of the heavy-quark potential [13][14][15][16][17][18][19][20] have been confirmed by first-principles nonperturbative Euclidean lattice QCD and classical real-time lattice QCD measurements [21][22][23][24][25][26][27]. Also, starting over a decade ago, phenomenological calculations of heavy-quarkonium suppression have included this effect [28][29][30][31][32][33][34][35][36][37]. These studies have provided strong indications that a self-consistent quantum mechanical description of heavy-quarkonium evolution in the QGP is now possible.…”

“…Recently, the QTraj code of Ref. [61], which implements a Monte Carlo quantum trajectories algorithm [62] for solving GKSL-type equations, was used to make phenomenological predictions for various heavy-ion collision bottomonium observ- [33][34][35]. For this purpose, the GKSL solver was coupled to a 3+1D viscous hydrodynamics code, which used smooth (optical) Glauber initial conditions [63][64][65].…”

“…For this purpose, the GKSL solver was coupled to a 3+1D viscous hydrodynamics code, which used smooth (optical) Glauber initial conditions [63][64][65]. Most recently, the OQS+pNRQCD framework was extended to next-to-leading order (NLO) in the binding energy over the temperature, allowing it to be applied at lower temperatures than the leading-order formalism [35]. In addition, the effect of fluctuating initial conditions in the hydrodynamic background was investigated using the NLO OQS+pNRQCD framework in Ref.…”