Bottomonium suppression and elliptic flow using Heavy Quarkonium Quantum Dynamics

TL;DR

This paper introduces Heavy Quarkonium Quantum Dynamics (HQQD), a new real-time quantum evolution framework, to study bottomonium suppression and flow in quark-gluon plasma, showing good agreement with experimental data and making new predictions.

Contribution

HQQD is a novel framework for real-time quantum evolution of heavy quarkonia in QGP, enabling detailed suppression and flow predictions with systematic uncertainty estimates.

Findings

HQQD predictions match experimental R_AA data for bottomonium.

Small elliptic flow for Upsilon(1s) due to path-length dependence.

Excited bottomonium states exhibit larger elliptic flow.

Abstract

We introduce a framework called Heavy Quarkonium Quantum Dynamics (HQQD) which can be used to compute the dynamical suppression of heavy quarkonia propagating in the quark-gluon plasma using real-time in-medium quantum evolution. Using HQQD we compute large sets of real-time solutions to the Schr\"{o}dinger equation using a realistic in-medium complex-valued potential. We sample 2 million quarkonia wave packet trajectories and evolve them through the QGP using HQQD to obtain their survival probabilities. The computation is performed using three different HQQD model parameter sets in order to estimate our systematic uncertainty. After taking into account final state feed down we compare our results to existing experimental data for the suppression and elliptic flow of bottomonium states and find that HQQD predictions are good agreement with available data for $R_{AA}$ as a function of $N_{\rm part}$ and $p_T$ collected at $\sqrt{s_{\rm NN}} =$ 5.02 TeV. In the case of $v_2$ for the various states, we find that the path-length dependence of $\Upsilon(1s)$ suppression results in quite small $v_2$ for $\Upsilon(1s)$. Our prediction for the integrated elliptic flow for $\Upsilon(1s)$ in the $10{-}90$\% centrality class, which now includes an estimate of the systematic error, is $v_2[\Upsilon(1s)]$ = 0.003 $\pm$ 0.0007 $\pm\,^{0.0006}_{0.0013}$. We also find that, due to their increased suppression, excited bottomonium states have a larger elliptic flow. Based on this observation we make predictions for $v_2[\Upsilon(2s)]$ and $v_2[\Upsilon(3s)]$ as a function of centrality and transverse momentum.