Data-Driven Analysis for the Bottomonium Potential in the Quark-Gluon Plasma

We present a data-driven analysis within a quantum evolutionary microscopic framework to constrain the in-medium bottomonium potential. In relativistic heavy-ion collisions, bottomonium bound states serve as invaluable probes of the quark-gluon plasma (QGP) owing to their negligible production in the QGP phase. Meanwhile, their non-relativistic nature allows a straightforward theoretical description via effective field theories such as potential models. Recent lattice QCD calculations of the bottomonium interaction potential have yielded qualitatively distinct results. These discrepancies motivate a data-driven extraction of the potential based on heavy-ion experiments. In this work, we perform a Bayesian analysis to constrain the bottomonium interaction potential. The relationship between potential parameters and observables is established by numerically solving the non-relativistic time-dependent Schr"odinger equation. By comparing these simulations with experimental measurements, our Bayesian framework provides the effective potential that is readily testable in future experiments.

💡 Research Summary

The authors present a comprehensive data‑driven framework that extracts the in‑medium bottomonium potential directly from heavy‑ion collision measurements using Bayesian inference. Recognizing that bottomonium states are produced almost exclusively before the quark‑gluon plasma (QGP) forms and that their large mass justifies a non‑relativistic description, they model the interaction with a temperature‑dependent complex static potential V(r,T)=V_R(r,T)−iV_I(r,T). The real part V_R is taken as a screened Cornell‑type (Helmholtz free‑energy) form, V_R=−α e^{−m_D r}/r+σ m_D(1−e^{−m_D r}), where the Debye mass m_D depends on a scaling parameter a_m and the local temperature. The imaginary part V_I, responsible for singlet‑to‑octet transitions and in‑medium dissociation, is parameterized as V_I/m_b= \bar T