From lattice QCD to in-medium heavy-quark interactions via deep learning

Abstract

Bottomonium states are key probes for 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 ($V_R(T,r)$) and imaginary ($V_I(T,r)$) 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, here, we obtain results for $V_R(T,r)$ and $V_I(T,r)$. The temperature dependence of $V_R(T,r)$ was found to be very mild between $T\approx0-330$~MeV. Meanwhile, $V_I(T,r)$ shows a rapid increase with $T$ and $r$, which is much larger than the perturbation theory-based expectations.