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Register a new userPhenomenological study of quarkonium suppression and the impact of the energy gap between singlets and octets
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Miguel \\'Angel Escobedo Espinosa
Publication date
2021
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English
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The study of heavy quarkonium suppression in heavy-ion collisions represents an important source of information about the properties of the quark-gluon plasma produced in such collisions. In a previous paper, we have considered how to model the evolution of a quarkonium in such a way that the solution of the resulting equations evolves toward the correct thermal equilibrium distribution for an homogeneous and static medium. We found that it is crucial to take into account the energy gap between singlet and octet configurations when the temperature is not much greater than this energy gap. In this manuscript, we explore in more detail the phenomenological consequences of this observation in the more realistic situation of an expanding system. We consider two different scenarios, based on the same approximation scheme, but on different choices of parameters. In the first case, we rely on a Hard Thermal Loop approximation, while the second case is based on a recent determination of the static potential in lattice QCD. In both cases, we compute the decay width and the nuclear modification factor, both taking the energy gap into account and ignoring it. We find that the impact on the predictions is as large in the expanding medium as it is in the static case. Our conclusion is that this energy gap should be taken into account in phenomenological studies.
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Many prior studies of in-medium quarkonium suppression have implicitly made use of an adiabatic approximation in which it was assumed that the heavy quark potential is a slowly varying function of time. In the adiabatic limit, one can separately determine the in-medium breakup rate and the medium time evolution, folding these together only at the end of the calculation. In this paper, we relax this assumption by solving the 3d Schrodinger equation in real-time in order to compute quarkonium suppression dynamically. We compare results obtained using the adiabatic approximation with real-time calculations for both harmonic oscillator and realistic complex heavy quark potentials. Using the latter, we find that, for the Upsilon(1s), the difference between the adiabatic approximation and full real-time evolution is at the few percent level, however, for the Upsilon(2s), we find that the correction can be as large as 18% in low temperature regions. For the J/Psi, we find a larger difference between the dynamical evolution and the adiabatic approximation, with the error reaching approximately 36%.
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.
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Several rotational invariant quantities for the lepton angular distributions in Drell-Yan and quarkonium production were derived several years ago, allowing the comparison between different experiments adopting different reference frames. Using an intuitive picture for describing the lepton angular distribution in these processes, we show how the rotational invariance of these quantities can be readily obtained. This approach can also be used to determine the rotational invariance or non-invariance of various quantities specifying the amount of violation for the Lam-Tung relation. While the violation of the Lam-Tung relation is often expressed by frame-dependent quantities, we note that alternative frame-independent quantities are preferred.
Quarkonium production in high-energy proton (deuteron)-nucleus collisions is investigated in the color glass condensate framework. We employ the color evaporation model assuming that the quark pair produced from dense small-x gluons in the nuclear target bounds into a quarkonium outside the target. The unintegrated gluon distribution at small Bjorken x in the nuclear target is treated with the Balitsky-Kovchegov equation with running coupling corrections. For the gluons in the proton, we examine two possible descriptions, unintegrated gluon distribution and ordinary collinear gluon distribution. We present the transverse momentum spectrum and nuclear modification factor for J/psi production at RHIC and LHC energies, and those for Upsilon(1S) at LHC energy, and discuss the nuclear modification factor and the momentum broadening by changing the rapidity and the initial saturation scale.
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