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

TL;DR

This paper derives a next-to-leading order Lindblad equation within pNRQCD to improve the modeling of heavy-quarkonium evolution in quark-gluon plasma, and applies numerical methods to compare with experimental data.

Contribution

We develop a NLO Lindblad equation for heavy-quarkonium dynamics in pNRQCD and implement numerical solutions to enhance phenomenological predictions.

Findings

NLO corrections improve the description of quarkonium suppression.

The quantum trajectories algorithm effectively solves the Lindblad equation.

Comparison with experimental data shows better agreement at NLO.

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 Schr\"odinger 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.