Efficient simulation of quarkonium master equation beyond the dipole approximation

TL;DR

This paper extends a quantum simulation code for quarkonium in quark-gluon plasma to accurately model larger quark-antiquark pairs at higher temperatures, improving the understanding of quarkonium behavior in heavy-ion collisions.

Contribution

It generalizes the quantum-trajectory simulation method to include medium effects at $rT \,\sim\, 1$ using HTL resummation, expanding applicability beyond the dipole approximation.

Findings

Extended the simulation to larger quarkonium states at higher temperatures.

Implemented new jump operators for color state transitions.

Discussed potential applications to excited bottomonium states.

Abstract

QTRAJ is a computer code that simulates the propagation of quarkonium in the quark-gluon plasma (QGP) based on the quantum-trajectory algorithm. This algorithm solves a master equation in which the quarkonium is treated as an open quantum system (OQS). A major advantage of this approach is that it turns a 3D spatial evolution for a density matrix into a 1D Schr\"odinger equation for a wavefunction with a non-hermitian Hamiltonian, drastically reducing the computational cost. So far, the interaction implemented in the master equation was obtained within the framework of potential non-relativistic QCD (pNRQCD), and restricted to the regime $rT \ll 1$, where $r$ is the size of the color dipole and $T$ is the temperature. In the environment produced in heavy-ion collisions (HIC's) this limit is accurate for $\Upsilon(1S)$, but the applicability to other quarkonium states is dubious. In the present study we generalize the above approach, extending it to the regime $rT\!\sim\! 1$ in the one-gluon exchange approximation, with proper Hard Thermal Loop (HTL) resummation of medium effects. This is done by implementing new jump operators connecting different color states of the $Q\bar Q$ pair and expanding them in plane waves, giving rise to a variation of the algorithm present in QTRAJ 1.0. Here we provide an overview of this approach comparing the $rT \ll 1$ and $rT\sim 1$ cases, and we discuss prospects for phenomenological application to excited states of bottomonium.