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, which can be characterized by real (VR(T, r)) and imaginary (VI(T, r)) potentials, as functions of temperature and spatial separation. 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 (DNN), here, we obtain model-independent results for VR(T, r) and VI(T, r). The temperature dependence of VR(T, r) was found to be very mild between T ≈ 0 − 330 MeV. Meanwhile, VI(T, r) shows rapid increase with T and r, which is much larger than the perturbation theory based expectations.
Highlights
In our recent work [33], we have developed a model-independent deep neural network (DNN)-based method and determine the r and T -dependence of the in-medium heavy quark potential starting from the lattice quantum chromodynamics (LQCD) results [31] 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 temperature can be used to extract VR(T, r) and VI(T, r) and, presently, DNN is probably the best tool achieve this in an unbiased fashion
Where b and W — called bias and weight, respectively — are the DNN parameters to be determined by fitting the LQCD masses and thermal widths [31]
Summary
In our recent work [33], we have developed a model-independent DNN-based method and determine the r and T -dependence of the in-medium heavy quark potential starting from the LQCD results [31] for the masses and thermal widths of up to 3S and 2P bottomonium states at various temperatures. The heavy quark potential can be extracted from the spectral functions of the thermal Wilson loop using nonperturbative LQCD calculations [26,27,28,29].
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