Abstract
We introduce a framework called Heavy Quarkonium Quantum Dynamics (HQQD) which can be used to compute the dynamical suppression of heavy quarkonia propagating in the quark-gluon plasma using real-time in-medium quantum evolution. Using HQQD we compute large sets of real-time solutions to the Schrödinger equation using a realistic in-medium complex-valued potential. We sample 2 million quarkonia wave packet trajectories and evolve them through the QGP using HQQD to obtain their survival probabilities. The computation is performed using three different HQQD model parameter sets in order to estimate our systematic uncertainty. After taking into account final state feed down we compare our results to existing experimental data for the suppression and elliptic flow of bottomonium states and find that HQQD predictions are good agreement with available data for RAA as a function of Npart and pT collected at sqrt{s_{mathrm{NN}}} = 5.02 TeV. In the case of v2 for the various states, we find that the path-length dependence of ϒ(1s) suppression results in quite small v2 for ϒ(1s). Our prediction for the integrated elliptic flow for ϒ(1s) in the 10−90% centrality class, which now includes an estimate of the systematic error, is v2[ϒ(1s)] = 0.003 ± 0.0007 ± {}_{0.0013}^{0.0006} . We also find that, due to their increased suppression, excited bottomonium states have a larger elliptic flow. Based on this observation we make predictions for v2[ϒ(2s)] and v2[ϒ(3s)] as a function of centrality and transverse momentum.
Highlights
(HQQD) which can be used to compute the dynamical suppression of heavy quarkonia propagating in the quark-gluon plasma using real-time in-medium quantum evolution
We have extended our previous work [44] by allowing for variation in the underlying Heavy Quarkonium Quantum Dynamics (HQQD) model parameters in order to assess the impact such variation has on HQQD predictions for RAA[Υ] and v2[Υ]
We provided more details concerning the numerical method used in HQQD and the method by which final state feed down effects were included
Summary
To begin we review the stochastic potential model with two noise sources for a heavy quark and anti-quark described in refs. [28, 31]. To begin we review the stochastic potential model with two noise sources for a heavy quark and anti-quark described in refs. The Hamiltonian consists of a screened potential V (r) and stochastic noise term Θ(r, t). Θ(r, t) is the sum of noise terms for the heavy quark, θ(x, t), and anti-quark, θ(x , t), which have the following correlations θ(x, t) = 0 , θ(x, t)θ(x , t ) = D(x − x )δ(t − t ). The stochastic Schrödinger equation for the noise averaged quarkonium wave function is,. From this expression, it can be seen that the imaginary part of the potential is related to the D-function via [V (r)] = D(r) − D(0)
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