Bottomonium suppression and elliptic flow using Heavy Quarkonium Quantum Dynamics

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 R AA as a function of N part and p T collected at √ s NN = 5.02 TeV. In the case of v 2 for the various states, we find that the path-length dependence of Υ(1s) suppression results in quite small v 2 for Υ(1s). Our prediction for the integrated elliptic flow for Υ(1s) in the 10−90% centrality class, which now includes an estimate on the systematic error, is v 2 [Υ(1s)] = 0.0026 ± 0.0007 ± 0.0005 0.001 . 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 v 2 [Υ(2s)] and v 2 [Υ(3s)] as a function of centrality and transverse momentum.

Effective Debye Screening Mass in an Anisotropic Quark Gluon Plasma

“…Our findings can be used to include the effect of momentum anisotropies on in-medium bound state evolution using real-time solution of the Schrödinger equation in a complex screened potential, see e.g. [34,35]. However, to do this properly one must prove that the same logic used herein for the real part of the potential can be applied to the imaginary part of the heavy-quark potential.…”

The imaginary part of the heavy-quark potential from real-time Yang-Mills dynamics

“…( 19). This functional form is motivated by the analytic leading-order perturbative HTL result (18) for which A HTL B HCL (β) ≈ 1.548 + 0.12 e −0.025β ,…”

“…For both our CYM lattice results and the HCL results, Im[V cl (r)]/g 2 T is plotted as a function of m D r, where we use the leading-order Debye mass m D,HCL calculated in HCL theory (15). On the right edge of the figure we indicate the asymptotic r → ∞ values obtained using both the dimensionally-regularized continuum HTL result (18) and the extrapolated N, β → ∞ HCL result with the parameters (24).…”

“…We can use it to compare to computations of κ with other methods. Let us first consider the continuum HTL result Im[V (2) (r)] of (18), which corresponds to the fitting form of the potential (22) with the parameter values (28). Plugging them into (35) leads to the expression…”

“…Fundamentally, the computation of the survival probability of a given bottomonium state can be cast into the framework of open quantum systems (OQS) in which there is a probe (bottomonium states) and medium (light quarks and gluons). Within the OQS framework, in order to describe the in-medium evolution of bottomonium states one must trace over the medium degrees of freedom and obtain evolution equations for the reduced density matrix of the system [6][7][8][9][10][11][12][13][14][15][16][17][18][19]. In the limit that the medium relaxation time scale and the intrinsic time scale of the probe are much smaller than the probe relaxation time scale, the resulting dynamical equation for the reduced density matrix can be cast into a so-called Lindblad form [20,21].…”