Bottomonium suppression at RHIC and LHC in an open quantum system approach

We present potential non-relativistic quantum chromodynamics (pNRQCD) predictions for bottomonium suppression in sqrt(sNN) = 200 GeV, 2.76 TeV, and 5.02 TeV heavy-ion collisions using an open quantum systems (OQS) description of the reduced heavy-quark anti-quark density matrix. Compared to prior OQS+pNRQCD studies we include the rapidity dependence of bottomonium production and evolution, allowing for a fully 3-dimensional description of bottomonium trajectories in the quark-gluon plasma. The underlying formalism used to compute the ground and excited state survival probabilities is based on a Lindblad equation that is accurate to next-to-leading order (NLO) in the binding energy over temperature. For the background evolution, we make use of a 3+1D viscous hydrodynamics code which reproduces soft hadron observables at all three collision energies. We find good agreement between NLO OQS+pNRQCD predictions and data taken at LHC energies, however, at RHIC energies, there is tension with recent bottomonium suppression measurements by the STAR collaboration.

💡 Research Summary

This paper presents a comprehensive theoretical investigation into the suppression of bottomonium states (bound states of bottom quarks and antiquarks) in heavy-ion collisions at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC). The study employs an advanced framework that combines the effective field theory of potential non-relativistic quantum chromodynamics (pNRQCD) with the formalism of open quantum systems (OQS).

The core objective is to compute the survival probability of bottomonium (Υ(1S, 2S, 3S), χ_b) as it propagates through the hot, dense quark-gluon plasma (QGP) created in these collisions. A key advancement over previous work is the full incorporation of momentum rapidity dependence in both the initial production and the subsequent in-medium evolution of bottomonium. This allows for a complete 3D description of its trajectory through the spatially and temporally evolving QGP.

The dynamical evolution of the heavy quark-antiquark pair’s internal quantum state is governed by a Lindblad master equation, derived within the OQS+pNRQCD framework. This equation is accurate to next-to-leading order (NLO) in the ratio of the bottomonium binding energy to the plasma temperature (E/T). The interaction with the QGP medium is encapsulated in two key transport coefficients: the heavy-quark momentum diffusion coefficient κ̂ and its dispersive counterpart γ̂. For this study, γ̂ is set to zero, while κ̂ is varied within ranges motivated by expectations from lattice QCD (3-4 at LHC energies, 4-5 at the lower RHIC energy).

The expanding QGP background is provided by state-of-the-art 3+1D viscous hydrodynamic simulations, which have been tuned to reproduce soft-hadron observables (like particle spectra and flow) at all three collision energies considered: 200 GeV at RHIC, and 2.76 TeV and 5.02 TeV at the LHC. Bottomonium trajectories are sampled according to initial production models and propagated eikonally through this hydrodynamical background. The Lindblad equation is then solved numerically along each trajectory using the quantum trajectories method, which includes the effects of quantum jumps (regeneration). Finally, the computed survival probabilities for directly produced states are convoluted with a feed-down matrix that accounts for the late-time decays of excited states into lower-lying ones, enabling direct comparison with experimental data via the nuclear modification factor R_AA.

The primary findings are:

1. Agreement at LHC Energies: The NLO OQS+pNRQCD predictions show excellent agreement with experimental data from the ALICE, ATLAS, and CMS collaborations for bottomonium R_AA as a function of collision centrality (number of participants, N_part) at 2.76 and 5.02 TeV. The model successfully describes the sequential suppression pattern (stronger suppression for more weakly bound excited states) and the 2S-to-1S yield ratio.
2. Tension at RHIC Energy: In stark contrast, at the lower RHIC energy of 200 GeV, the model predictions for Υ(1S) and Υ(2S) R_AA are significantly higher (indicating less suppression) than the recent, precise measurements from the STAR collaboration. This discrepancy persists regardless of whether the rapidity dependence is included in the calculation.
3. Role of 3D Dynamics: Including the full 3D rapidity-dependent evolution is found to improve the agreement with LHC data, highlighting the importance of a complete geometrical treatment.

The paper concludes that while the OQS+pNRQCD framework is highly successful in describing bottomonium suppression at LHC energies, its application at the lower RHIC energy reveals a significant tension with data. This suggests that the properties of the QGP or the theoretical assumptions (like the scale hierarchy E « T) might differ in important ways at the lower temperatures prevalent at RHIC. The authors propose that future work should focus on a more precise, temperature-dependent determination of the transport coefficients from lattice QCD and a critical re-examination of the framework’s applicability at lower collision energies.