Bottomonium suppression and elliptic flow from real-time quantum evolution

We compute the suppression and elliptic flow of bottomonium using real-time solutions to the Schr\"{o}dinger equation with a realistic in-medium complex-valued potential. To model the initial production, we assume that, in the limit of heavy quark masses, the wave-function can be described by a lattice-smeared (Gaussian) Dirac delta wave-function. The resulting final-state quantum-mechanical overlaps provide the survival probability of all bottomonium eigenstates. Our results are in good agreement with available data for $R_{AA}$ as a function of $N_{\rm part}$ and $p_T$ collected at $\sqrt{s_{\rm NN}} =$ 5.02 TeV. In the case of $v_2$ for the various states, we find that the path-length dependence of $\Upsilon(1s)$ suppression results in quite small $v_2$ for $\Upsilon(1s)$. Our prediction for the integrated elliptic flow for $\Upsilon(1s)$ in the $10{-}90$% centrality class is $v_2[\Upsilon(1s)] = 0.0026 \pm 0.0007$. We additionally find that, due to their increased suppression, excited bottomonium states have a larger elliptic flow and we make predictions for $v_2[\Upsilon(2s)]$ and $v_2[\Upsilon(3s)]$ as a function of centrality and transverse momentum. Similar to prior studies, we find that it is possible for bottomonium states to have negative $v_2$ at low transverse momentum.