Probing hot QCD medium with heavy quarkonium in small and large collision systems

The yield ratios of different heavy quarkonium states serve as sensitive probes of final-state interactions in relativistic nuclear collisions, as they effectively cancel out common cold-nuclear-matter effects. To quantify hot QCD medium effects in small collision systems, such as proton-nucleus collisions, we employ a time-dependent Schrodinger equation framework to consistently simulate the real-time evolution of both bottomonium and charmonium states in the presence of in-medium complex heavy-quark potentials. In $p$-Pb collisions at $\sqrt{s_{\mathrm{N}\mathrm{N}}}=8.16$ TeV, our model successfully describes the observed suppression in the yield ratios of excited-to-ground states-specifically $\mathrm{{\rm Y}}(nS)\mathrm{/}\mathrm{{\rm Y}}(1S)$ and $\psi (2S)\mathrm{/}J\mathrm{/}\psi$-as a function of charged-particle multiplicity. This agreement supports the formation of a transient, hot QCD medium in small systems. Furthermore, the framework is employed to study the ratio of bottomonium nuclear modification factors in $\sqrt{s_{\mathrm{N}\mathrm{N}}}=5.02$ TeV Pb-Pb collisions, where hot medium effects become stronger. By establishing a unified description across two distinct heavy-quark flavors and different collision systems, our study indicates that the yield ratio of bottomonium states serves as a clean probe of the hot QCD medium generated in small collision systems.