Unified Extraction of In-Medium Heavy Quark Potentials from RHIC to LHC Energies via Deep Learning

TL;DR

This paper employs deep learning with Bayesian methods to extract the in-medium heavy quark potential from bottomonium suppression data across RHIC and LHC energies, revealing insights into the real and imaginary components of the potential.

Contribution

It introduces a novel deep learning framework combining CNNs and Bayesian inference to simultaneously extract and analyze the heavy quark potential from experimental data across multiple collision energies.

Findings

The real part of the potential remains close to the vacuum Cornell form across energies.

The imaginary part of the potential is strongly constrained and dominates suppression effects.

The methodology enables a unified analysis of heavy quark interactions in hot QCD media.

Abstract

We use deep learning under Bayesian perspective to quantitatively extract the in-medium heavy quark (HQ) potential from bottomonium nuclear modification factors ($R_{AA}$) measured across multiple heavy ion collision systems at the Large Hadron Collider (LHC) and the Relativistic Heavy-Ion Collider (RHIC). The in-medium HQ potential, comprising both a real and imaginary part, is parameterized and incorporated into a time-dependent Schr\"odinger equation to model the wave function evolution of $b\bar{b}$ dipoles within a hydrodynamically evolving hot QCD medium. We construct Convolutional Neural Networks (CNNs) to capture the non-linear correspondence between the heavy quark potential $V(T,r)$ and the bottomonium $R_{AA}$ for Pb-Pb collisions at 5.02 TeV and 2.76 TeV, and Au-Au collisions at 200 GeV. Training datasets are generated by sampling the potential parameters and are further augmented using Principal Component Analysis (PCA) and Gaussian Process Regression (GPR). After validating the stability and correctness of the CNNs, we employ Stochastic Gradient Langevin Dynamics (SGLD) to perform a simultaneous Bayesian inverse extraction of the optimal potential parameters and their posterior distributions using experimental data of bottomonium $R_{AA}$ in both LHC and RHIC energies. Our joint multi-energy extraction suggests that, within the present parametrization and hydrodynamic background, the real part of the in-medium potential remains close to the vacuum Cornell form, corresponding to a relatively weak screened Debye mass across RHIC to LHC energies. By contrast, the imaginary part is more strongly constrained by the data and provides the dominant contribution to bottomonium suppression from RHIC to LHC energies.