Bottomonium suppression and elliptic flow in an anisotropic quark-gluon plasma using the quantum trajectories method

TL;DR

This work develops a framework to study bottomonium in a momentum-space anisotropic QGP using the quantum trajectories method with a novel anisotropic complex potential. The real part extends the KMS potential via an anisotropic Debye mass, while the imaginary part is constructed to capture both small- and large-ξ behavior, with a smooth interpolating model. Real-time Schrödinger evolution on a 3+1D hydrodynamic background yields R_AA, double ratios, and v_2 for Υ(1S,2S,3S) including feed-down, reproducing sequential suppression and nonzero elliptic flow in agreement with ALICE/ATLAS/CMS, though Υ(2S) double-ratio tensions remain. The results underscore the role of path-length dependent suppression and medium anisotropy in quarkonium phenomenology and point to refinements in the imaginary-part treatment and hydrodynamic fluctuations for future work. Overall, QTraj-Aniso provides a robust tool for real-time tomography of the QGP using heavy quarkonia.

Abstract

We study bottomonium dynamics in a momentum-space anisotropic quark-gluon plasma (QGP) using the quantum trajectories (QTraj) framework. The real part of the heavy-quark potential is obtained from a minimal extension of the Karsch-Mehr-Satz (KMS) potential, while the angle-averaged imaginary part is derived to leading order in the anisotropy parameter $ξ$ and modeled to interpolate smoothly between the small- and large -$ξ$ regimes. The resulting anisotropic complex potential is used to solve the real-time Schrödinger equation using QTraj for the evolution of bottomonium in heavy-ion collisions. Nuclear modification factors $R_{AA}$, double ratios, and elliptic flow coefficients $v_2$ for the $Υ(1S)$, $Υ(2S)$, and $Υ(3S)$ states are computed, including feed-down contributions, in Pb-Pb collisions at $\sqrt{s_{NN}} = 5.02 \, \text{TeV}$. The QTraj-Aniso predictions successfully reproduce the observed sequential suppression pattern and non-zero elliptic flow, showing good agreement with experimental measurements from the ALICE, ATLAS, and CMS collaborations and demonstrating the relevance of path-length dependent suppression and medium anisotropy in quarkonium phenomenology.

Figures (9)

• Figure 1: Nuclear suppression factor, $R_{AA}$, of bottomonium s-wave states as a function of $N_\text{part}$ (left panel) and $p_T$ (right panel). The solid, short-dashed, and dashed lines show the predictions of QTraj Aniso. The experimental measurements shown are from the ALICE ALICE:2020wwx, ATLAS ATLAS5TeV, and CMS Sirunyan:2018nszCMS-PAS-HIN-21-007 collaborations. Experimental error bars shown were obtained by adding statistical and systematic uncertainties in quadrature.
• Figure 2: Double ratio $[\Upsilon(2s)/\Upsilon(1s)]_\text{PbPb}/[\Upsilon(2s)/\Upsilon(1s)]_\text{pp}$ as a function of $N_\text{part}$ (left panel) and $p_T$ (right panel). The solid line shows the prediction of QTraj-Aniso. The experimental measurements shown are from the ATLAS ATLAS5TeV and CMS Sirunyan:2018nszCMS-PAS-HIN-21-007 collaborations.
• Figure 3: Double ratio $[\Upsilon(3S)/\Upsilon(1S)]_\text{PbPb}/[\Upsilon(3S)/\Upsilon(1S)]_\text{pp}$ as a function of $N_\text{part}$. Line styles and experimental data sources are the same as Fig. \ref{['fig02']}.
• Figure 4: Double ratio $[\Upsilon(3S)/\Upsilon(2S)]_\text{PbPb}/[\Upsilon(3S)/\Upsilon(2S)]_\text{pp}$ as a function of $N_\text{part}$ (left panel) and $p_T$ (right panel). Line styles are the same as Fig. \ref{['fig02']}. The centrality classes used were 0-30%, 30-50%, 50-70%, and 70-90%. Experimental data are from Ref. CMS-PAS-HIN-21-007.
• Figure 5: Integrated nuclear suppression factors $R_{AA}$ (left panel) and double ratios (right panel) for bottomonium s-wave states. The open blue circles (QTraj-Aniso) represent theoretical calculations, while the filled markers show experimental results from ALICE ALICE:2020wwx, ATLAS ATLAS5TeV, and CMS Sirunyan:2018nszCMS-PAS-HIN-21-007 collaborations with statistical and systematic uncertainties indicated separately.