⚛️ nuclear theory

Bottomonium transport in the sQGP at RHIC and the LHC

This paper employs kinetic rate equations within (3+1)D viscous hydrodynamic simulations to demonstrate that while rapid inelastic suppression and regeneration dominate bottomonium dynamics at LHC energies, the smaller regeneration effect at RHIC, combined with nuclear absorption, explains why $\Upsilon(1S)$ production magnitudes are comparable at both colliders despite the LHC's higher temperatures.

Original authors: Biaogang Wu, Jacob Boyd, Ralf Rapp

Published 2026-08-24

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Biaogang Wu, Jacob Boyd, Ralf Rapp

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Deep within the heart of a particle accelerator, when two heavy atomic nuclei smash together at nearly the speed of light, they create a fleeting, superheated soup of matter known as the quark-gluon plasma. This state of existence, which filled the universe mere microseconds after the Big Bang, is so hot and dense that the protons and neutrons inside the nuclei melt apart, freeing their constituent quarks and gluons to roam in a chaotic, deconfined state. Scientists study this primordial fireball to understand how the strong force, the fundamental glue that holds matter together, behaves under extreme conditions. A particularly sensitive probe for this environment is the bottomonium, a particle made of a heavy bottom quark and its antimatter partner, the bottom antiquark, bound tightly together. Because these particles are so heavy, they are created in the very first instant of the collision, before the fireball even forms. As they travel through the expanding plasma, they face a gauntlet of intense heat and pressure that can rip them apart. By watching which bottomonium particles survive and which are destroyed, physicists can map the temperature and density of the invisible fireball, much like a thermometer measuring the heat of a furnace.

For years, a puzzling contradiction has lingered in the data collected from these high-energy collisions. Experiments at the Large Hadron Collider in Europe, where temperatures reach staggering levels, showed that the most tightly bound bottomonium particles were suppressed, or destroyed, to a certain degree. Surprisingly, experiments at the Relativistic Heavy Ion Collider in the United States, where the temperatures are significantly lower, showed a similar level of suppression. If the plasma were simply a destructive oven, one would expect the cooler fireball at the American facility to leave more particles intact. The fact that the destruction rates were comparable suggested that the standard model of a simple, one-way destruction process was incomplete. Something else must be happening to replenish the particles that were lost.

A new study by researchers at Texas A&M University and Kent State University has provided a compelling explanation for this mystery by simulating the entire life cycle of these particles within the fireball. Instead of treating the plasma as a static barrier that only destroys, the team modeled it as a dynamic, living environment where particles are constantly being broken apart and reformed. They used a sophisticated computer model that combines the fluid-like expansion of the plasma with the statistical laws of particle interactions. In their simulation, the bottom quarks and antiquarks, once ripped from their original partners, do not simply vanish. Instead, they wander through the hot medium, slowed down by the intense interactions with the surrounding particles. Because the plasma is so dense and strongly coupled, these wandering quarks have a surprisingly high chance of bumping into each other again and recombining into a new bottomonium particle. This process of reformation, or regeneration, acts as a counterbalance to the destruction.

The researchers tracked nine different types of bottomonium states, ranging from the most stable ground state to highly excited, fragile versions. Their calculations revealed that at the extreme temperatures of the Large Hadron Collider, the excited states are destroyed almost instantly. However, the high reaction rates in this strongly coupled plasma mean that these excited states are also regenerated very quickly, often becoming the primary source of the particles observed in the final detectors. Even the most stable ground state, which was thought to survive mostly from its original creation, receives a significant boost from this regeneration process in central collisions. The key finding is that the plasma is not just a destructive force; it is a bustling marketplace where particles are constantly being unmade and remade.

When the team applied this same model to the lower-energy collisions at the Relativistic Heavy Ion Collider, the picture changed in a way that resolved the long-standing puzzle. At these lower temperatures, the rate of regeneration is much slower. Consequently, the bottomonium particles that survive are mostly the ones that were created at the very beginning and managed to escape destruction. However, the researchers also accounted for a different effect that occurs at lower energies: as the particles form, they must pass through the dense nuclei of the colliding atoms before the fireball even ignites. This "nuclear absorption" acts as a filter, destroying a portion of the initial particles. The study found that the combination of less regeneration and this extra initial destruction perfectly balances out the numbers. The result is that the final number of surviving particles at the lower-energy facility ends up looking remarkably similar to the number at the higher-energy facility, despite the vast difference in temperature.

This work suggests that the behavior of the quark-gluon plasma is governed by a delicate equilibrium between destruction and creation, driven by the intense interactions of a strongly coupled system. The researchers did not just propose this idea; they built a detailed, parameter-free simulation that reproduces the experimental data from both facilities with high precision. By showing that the same physical laws can explain the results across such different energy scales, the study offers a unified view of how matter behaves in the most extreme conditions imaginable. It confirms that the plasma is a strongly interacting fluid where the heavy quarks are not merely passive victims of heat, but active participants in a continuous cycle of breaking and rebuilding, a process that ultimately determines what we see when the fireball cools and fades away.

Technical Summary: Bottomonium Transport in the sQGP at RHIC and the LHC

Problem Statement
The production of bottomonium ( $\Upsilon$ ) states in ultra-relativistic heavy-ion collisions serves as a critical probe of the Quark-Gluon Plasma (QGP). While charmonium production exhibits a transition from suppression at lower energies (SPS, RHIC) to enhancement at the LHC due to regeneration, bottomonium remains strongly suppressed even at LHC energies, particularly for excited states. This has traditionally been interpreted as sequential suppression based on dissociation temperatures. However, a significant theoretical tension exists: experimental data from RHIC (Au-Au at 200 GeV) shows $\Upsilon(1S)$ suppression levels comparable to those at the LHC (Pb-Pb at 5.02 TeV), despite the LHC QGP reaching significantly higher initial temperatures. Pure suppression models struggle to explain this, and previous transport calculations have yielded conflicting results regarding the magnitude of the regeneration component.

Methodology
The authors implement a kinetic rate equation into a (3+1)D anisotropic hydrodynamic (aHydro) simulation to model bottomonium transport. The framework couples microscopic reaction rates with macroscopic hydrodynamic evolution without introducing tunable parameters for the core transport mechanisms.

Reaction Rates: The inelastic reaction rates ( $\Gamma_Y$ ) and equilibrium limits are derived from a thermodynamic T-matrix formalism. The input potential is constrained by state-of-the-art Wilson line correlators from lattice QCD (lQCD). This approach yields large collisional widths characteristic of a strongly coupled QGP (sQGP), resulting in significantly higher reaction rates than perturbative approaches.
Hydrodynamic Evolution: The QGP expansion is modeled using (3+1)D aHydro, tuned to reproduce soft-hadron observables at both RHIC and LHC. The equation of state (EoS) is consistent with lQCD data. Bottomonium trajectories are sampled based on momentum distributions, and local temperatures are recorded along these paths to compute survival probabilities.
Regeneration Mechanism: The regeneration component is calculated as the inhomogeneous solution to the rate equation. The equilibrium limit ( $N^{eq}_Y$ $N_{Y}^{e q}$ ) is evaluated using a space-time-dependent medium. Key corrections include:
- Correlation Volume: Enforcing local $b\bar{b}$ conservation after point-like production.
- Thermal Relaxation: Accounting for the incomplete thermalization of $b$ -quarks via a relaxation time correction.
- Escape Effects: Calculating the fraction of $b\bar{b}$ pairs remaining within the active fireball volume ( $T > T_h$ ) over time.
- Coalescence: Transverse-momentum ( $p_T$ ) spectra for regenerated states are generated using an Instantaneous Coalescence Model (ICM) based on transported $b$ -quark distributions.
Cold Nuclear Matter (CNM) Effects: The model incorporates nuclear shadowing (using EPPS21 nPDFs) and nuclear absorption (via an effective cross-section $\sigma_{abs}$ ), the latter being particularly relevant for RHIC energies where Lorentz contraction is less extreme.
Feed-down: A feed-down matrix constructed from experimental branching fractions is used to convert direct production yields into inclusive observables, covering nine $\Upsilon$ states (up to 3S and 2P).

Key Contributions and Results

LHC Observables (Pb-Pb at 5.02 TeV):
- The large reaction rates derived from the T-matrix formalism lead to rapid suppression of excited states ( $\Upsilon(2S), \Upsilon(3S)$ ), rendering regeneration their dominant source even in peripheral collisions.
- For the ground state $\Upsilon(1S)$ , a significant primordial component survives in central collisions, but regeneration contributes substantially to the total yield.
- The model reproduces centrality and $p_T$ dependence data from CMS, ATLAS, and ALICE with fair agreement.
- Double ratios (e.g., $\Upsilon(2S)/\Upsilon(1S)$ ) are sensitive to the interplay of suppression and regeneration; the inclusion of regeneration improves agreement with data, particularly for excited states.
- A benchmark comparison with previous perturbative rates shows that the new non-perturbative rates are necessary to achieve the observed level of suppression for excited states.
RHIC Observables (Au-Au at 200 GeV) and the "Puzzle":
- At RHIC, the fireball is cooler and shorter-lived, leading to overall less regeneration compared to the LHC.
- For $\Upsilon(1S)$ , the primordial component remains dominant across all centralities.
- The paper addresses the puzzle of comparable $\Upsilon(1S)$ suppression at RHIC and LHC. The authors find that while regeneration is smaller at RHIC, the inclusion of a moderate nuclear absorption cross-section ( $\sigma_{abs} \approx 3$ mb) reduces the primordial yield sufficiently to match the observed suppression level.
- This suggests that the similar suppression levels are not due to a "temperature-sequential" suppression mechanism but rather a balance between reduced regeneration and nuclear absorption at RHIC, versus higher regeneration and lower absorption at the LHC.
Transverse Momentum Spectra:
- Regeneration is the leading source at low $p_T$ ( $\lesssim 10$ GeV) for all states, with the regenerated component becoming softer for higher excited states.
- The model underestimates data at high $p_T$ ( $\gtrsim 10$ GeV), a tension the authors attribute to potential changes in the production mechanism (e.g., gluon fragmentation) or space-momentum correlations not fully captured in the current coalescence model.

Significance and Claims
The paper claims that the large reaction rates inherent to a strongly coupled QGP, derived from a consistent T-matrix and lQCD framework, necessitate a substantial regeneration component for bottomonium yields, particularly for excited states. The primary significance of this work is the resolution of the RHIC $\Upsilon(1S)$ suppression puzzle: the comparable suppression levels at RHIC and LHC are explained not by identical suppression mechanisms, but by a combination of significantly reduced regeneration and the inclusion of nuclear absorption effects at RHIC.

The authors emphasize that their framework relies on non-perturbative inputs constrained by lQCD and does not use tunable parameters for the hydrodynamic evolution or reaction rates. While the model achieves fair agreement with experimental data across centrality and $p_T$ , the authors modestly acknowledge unresolved tensions at high $p_T$ and the schematic nature of certain approximations (e.g., thermal relaxation and formation times), identifying these as targets for future refinement.

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