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Register a new userBottomonium suppression in an open quantum system using the quantum trajectories method
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We solve the Lindblad equation describing the Brownian motion of a Coulombic heavy quark-antiquark pair in a strongly coupled quark-gluon plasma using the highly efficient Monte Carlo wave-function method. The Lindblad equation has been derived in the framework of pNRQCD and fully accounts for the quantum and non-Abelian nature of the system. The hydrodynamics of the plasma is realistically implemented through a 3+1D dissipative hydrodynamics code. We compute the bottomonium nuclear modification factor and compare with the most recent LHC data. The computation does not rely on any free parameter, as it depends on two transport coefficients that have been evaluated independently in lattice QCD. Our final results, which include late-time feed down of excited states, agree well with the available data from LHC 5.02 TeV PbPb collisions.
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We report predictions for the suppression and elliptic flow of the $Upsilon(1S)$, $Upsilon(2S)$, and $Upsilon(3S)$ as a function of centrality and transverse momentum in ultra-relativistic heavy-ion collisions. We obtain our predictions by numerically solving a Lindblad equation for the evolution of the heavy-quarkonium reduced density matrix derived using potential nonrelativistic QCD and the formalism of open quantum systems. To numerically solve the Lindblad equation, we make use of a stochastic unraveling called the quantum trajectories algorithm. This unraveling allows us to solve the Lindblad evolution equation efficiently on large lattices with no angular momentum cutoff. The resulting evolution describes the full 3D quantum and non-abelian evolution of the reduced density matrix for bottomonium states. We expand upon our previous work by treating differential observables and elliptic flow; this is made possible by a newly implemented Monte-Carlo sampling of physical trajectories. Our final results are compared to experimental data collected in $sqrt{s_{NN}} = 5.02$ TeV Pb-Pb collisions by the ALICE, ATLAS, and CMS collaborations.
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 Schr{o}dinger 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 $N_{rm part}$ 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, which now includes an estimate of the systematic error, is $v_2[Upsilon(1s)]$ = 0.003 $pm$ 0.0007 $pm,^{0.0006}_{0.0013}$. 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 $v_2[Upsilon(2s)]$ and $v_2[Upsilon(3s)]$ as a function of centrality and transverse momentum.
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.
I review recent applications of the open quantum system framework in the understanding of quarkonium suppression in heavy-ion collisions, which has been used as a probe of the quark-gluon plasma for decades. The derivation of the Lindblad equations for quarkonium in both the quantum Brownian motion and the quantum optical limits and their semiclassical counterparts is explained. The hierarchy of time scales assumed in the derivation is justified from the separation of energy scales in nonrelativistic effective field theories of QCD. Physical implications of the open quantum system approach are also discussed. Finally, I list some open questions for future studies.
We utilize the technology of open quantum systems in conjunction with the recently developed effective field theory for forward scattering to address the question of massless jet propagation through a weakly-coupled quark-gluon plasma in thermal equilibrium. We discuss various possible hierarchies of scales that may appear in this problem, by comparing thermal scales of the plasma with relevant scales in the effective field theory. Starting from the Lindblad equation, we derive and solve a master equation for the transverse momentum distribution of a massless quark jet, at leading orders both in the strong coupling and in the power counting of the effective field theory. Markovian approximation is justified in the weak coupling limit. Using the solution to the master equation, we study the transverse momentum broadening of a jet as a function of the plasma temperature and the time of propagation. We discuss the physical origin of infrared sensitivity that arises in the solution and a way to handle it in the effective field theory formulation. We suspect that the final measurement constraint can only cut-off leading infrared singularities and the solution to the Markovian master equation resums a logarithmic series. This work is a stepping stone towards understanding jet quenching and jet substructure observables on both light and heavy quark jets as probes of the quark-gluon plasma.
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