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Abstract
Bottomonium states are key probes for experimental studies of the quark-gluon plasma (QGP) created in high-energy nuclear collisions. Theoretical models of bottomonium productions in high-energy nuclear collisions rely on the in-medium interactions between the bottom and antibottom quarks. The latter can be characterized by the temperature ($T$) dependent potential, with real ($V_R(T,r)$) and imaginary ($V_I(T,r)$) parts, as a function of the spatial separation ($r$). Recently, the masses and thermal widths of up to $3S$ and $2P$ bottomonium states in QGP were calculated using lattice quantum chromodynamics (LQCD). Starting from these LQCD results and through a novel application of deep neural network, here, we obtain $V_R(T,r)$ and $V_I(T,r)$ in a model-independent fashion. The temperature dependence of $V_R(T,r)$ was found to be very mild between $T\approx0-334$~MeV. For $T=151-334$~MeV, $V_I(T,r)$ shows a rapid increase with $T$ and $r$, which is much larger than the perturbation-theory-based expectations.
Highlights
In-medium modifications of quarkonium states, i.e., bound states of a heavy charm or bottom quark and its antiquark, are sensitive probes of the quark-gluon plasma (QGP) produced in high-energy nuclear collisions [1–13]
Sequential suppression patterns among the Υð1SÞ, Υð2SÞ, and Υð3SÞ states have been observed in heavy ion collision experiments [14–17]. Theoretical understanding of these experimental observations relies on effective field theories (EFTs), which naturally lead to an open-quantum-systembased treatment of both open and hidden bottom states in QGP
We introduce a modelindependent deep-neural-network-based (DNN-based) method and determine the r and T-dependence of the inmedium heavy quark potential starting from the lattice quantum chromodynamics (LQCD) results [33] for the masses and thermal widths of up to 3S and 2P bottomonium states at various temperatures
Summary
In-medium modifications of quarkonium states, i.e., bound states of a heavy charm or bottom quark and its antiquark, are sensitive probes of the quark-gluon plasma (QGP) produced in high-energy nuclear collisions [1–13]. As we shall see later, one-loop HTL-motivated functional forms of VRðT; rÞ and VIðT; rÞ are not compatible with these LQCD results This observation calls for a model-independent treatment of the in-medium heavy quark potential. We introduce a modelindependent deep-neural-network-based (DNN-based) method and determine the r and T-dependence of the inmedium heavy quark potential starting from the LQCD results [33] for the masses and thermal widths of up to 3S and 2P bottomonium states at various temperatures. LQCD results for the masses and thermal widths of multiple bottomonium states at different temperatures can be used to extract VRðT; rÞ and VIðT; rÞ and, presently, a DNN is probably the best tool to achieve this in an unbiased fashion To this goal, we develop a new method to optimize the deep neural network coupled with the Schrödinger equation. To discuss the connection between the imaginary energy and the width extracted in lattice QCD
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