Observation of charmonium sequential suppression in heavy-ion collisions at the Relativistic Heavy Ion Collider

Using the STAR experiment at RHIC, researchers observed significant sequential suppression of charmonium states in Ru+Ru and Zr+Zr collisions at 200 GeV, demonstrating that the larger $\psi$(2S) meson is suppressed more strongly than the J/$\psi$ meson with a 5.6 standard deviation significance.

The Gist

Here is an explanation of the paper using simple language and everyday analogies.

The Big Picture: Cooking a "Particle Soup"

Imagine you are a chef trying to understand what happens inside a giant, super-hot pot of soup. In the world of physics, this "soup" is called Quark-Gluon Plasma (QGP). It's a state of matter that existed just fractions of a second after the Big Bang, where the tiny building blocks of atoms (quarks and gluons) are free-floating instead of being stuck together inside particles like protons and neutrons.

To study this soup, scientists at the Relativistic Heavy Ion Collider (RHIC) smash two heavy atoms together at nearly the speed of light. This creates a tiny, fleeting drop of this super-hot soup.

The Test Subjects: The "Heavy" and the "Light"

To see how the soup affects things, the scientists use two specific types of "test particles" made of heavy charm quarks. Think of them as two different kinds of balloons floating in a hot wind:

1. The J/ψ (J-Psi): A smaller, tighter, and more durable balloon. It can withstand a bit more heat before popping.
2. The ψ(2S) (Psi-2S): A larger, fluffier, and more fragile balloon. Because it is bigger and looser, it pops much easier in the heat.

The Theory: If you throw both balloons into a hot oven (the QGP), the fragile, big one (ψ(2S)) should pop (dissociate) much more often than the tough, small one (J/ψ). This is called sequential suppression.

The Experiment: Ru vs. Zr

In this specific study, the STAR collaboration didn't use the usual heavy lead atoms. Instead, they used two slightly lighter elements: Ruthenium (Ru) and Zirconium (Zr).

• Why? It's like testing your oven with two slightly different sizes of baking pans. By using these smaller atoms, the scientists could see how the "soup" behaves when the collision isn't as massive as the usual lead collisions. They wanted to see if the "fragile balloon" still pops more than the "tough balloon" in these smaller, slightly different conditions.

The Method: The "Machine Learning Detective"

Detecting these particles is incredibly hard. When the atoms smash, they create billions of other particles that look like noise. Finding the J/ψ and ψ(2S) is like trying to find two specific, rare coins in a massive pile of sand.

To solve this, the scientists used a Machine Learning tool (specifically an algorithm called XGBoost).

• The Analogy: Imagine you have a pile of mixed-up photos. Some show the rare coins (signal), and most show just sand (background). You train a smart computer to look at the photos and learn the subtle differences between the coins and the sand. Once trained, the computer can scan the whole pile and point out the coins with high confidence.

The Results: The Balloons Definitely Popped

The scientists looked at the ratio of the fragile balloons (ψ(2S)) to the tough ones (J/ψ) after the collision.

1. The Expectation: In a normal collision (like two cars gently bumping), you expect to see a certain ratio of fragile to tough balloons.
2. The Reality: In the heavy-ion collisions (the "soup"), they found significantly fewer fragile balloons than expected.
   • The ratio dropped to about 0.41. This means that for every 100 tough balloons you'd expect, you only found about 41 fragile ones.
   • This difference is huge (statistically speaking, it's a "5.6 sigma" result, which is like flipping a coin 10 times and getting heads every single time—it's not a fluke).

What this means: The hot soup definitely "popped" the fragile ψ(2S) balloons much more than the tough J/ψ balloons. This confirms that the QGP is a real, hot environment that destroys larger particles more easily.

The "Cold" vs. "Hot" Mystery

There was a worry: Maybe the balloons popped not because of the hot soup, but just because they had to squeeze through the heavy atoms before the soup even formed (this is called "Cold Nuclear Matter" effects).

• The Check: The scientists compared their results to what happens when a single proton hits a heavy atom (which creates no soup, just "cold" effects).
• The Verdict: The suppression they saw in the heavy collisions was much stronger than in the "cold" collisions. This proves that the "hot soup" (QGP) is the main culprit, not just the heavy atoms themselves.

The "Central" vs. "Peripheral" Trend

The scientists also looked at how "head-on" the collisions were:

• Central Collisions: A direct, head-on smash (like hitting a nail with a hammer). This creates the biggest, hottest soup.
• Peripheral Collisions: A glancing blow (like two cars brushing past each other). This creates a smaller, cooler soup.

They saw a hint that the fragile balloons were suppressed even more in the head-on collisions than in the glancing ones. This makes sense: the bigger the soup, the more likely the fragile balloon is to pop.

Why Does This Matter?

This paper is important because:

1. It fills a gap: Previous studies looked at very heavy collisions (Lead) at very high energies. This study looked at lighter collisions (Ru/Zr) at a medium energy. It connects the dots between different types of experiments.
2. It proves the theory: It provides strong, clear evidence that the "sequential suppression" (big things pop before small things) is happening in these smaller systems.
3. It refines the map: By seeing how the particles behave in these specific conditions, physicists can better understand the "recipe" of the Quark-Gluon Plasma—how hot it gets, how long it lasts, and how it flows.

In short: The scientists smashed atoms together, used AI to find rare particles, and proved that in the resulting super-hot soup, the "fragile" particles get destroyed much more than the "tough" ones. This confirms our understanding of how the universe behaved just after the Big Bang.

Technical Summary

Here is a detailed technical summary of the paper "Observation of charmonium sequential suppression in heavy-ion collisions at the Relativistic Heavy Ion Collider" by the STAR Collaboration.

1. Problem and Scientific Context

The primary goal of this research is to investigate the properties of the Quark-Gluon Plasma (QGP), a state of matter where quarks and gluons are deconfined, formed in ultra-relativistic heavy-ion collisions.

• The Probe: Charmonium states (bound states of a charm quark and its antiquark), specifically $J/\psi$ and $\psi(2S)$, serve as sensitive probes.
• The Mechanism: In the QGP, charmonia are subject to two competing processes:
  1. Dissociation: The color screening effect of the QGP breaks the bound state.
  2. Regeneration: Deconfined charm quarks and antiquarks recombine to form new charmonia.
• Sequential Suppression: The $\psi(2S)$ meson has a larger spatial radius ($\approx 1.8$ times that of $J/\psi$) and a lower binding energy. Theoretical models predict that $\psi(2S)$ should dissociate at lower temperatures and be more strongly suppressed than $J/\psi$ in the QGP.
• The Gap: Previous measurements of the $\psi(2S)$ to $J/\psi$ ratio existed at low energy ($\sqrt{s_{NN}} = 17.3$ GeV) and very high energy ($5.02$ TeV). There was a lack of data at the intermediate energy of 200 GeV and in smaller collision systems (Ru+Ru and Zr+Zr) compared to the standard Pb+Pb systems. Understanding the interplay between dissociation and regeneration at this energy and system size is crucial for constraining QGP transport properties.

2. Methodology

The study utilized data collected by the STAR experiment at the Relativistic Heavy Ion Collider (RHIC).

• Dataset: Approximately 1.8 billion $^{96}\text{Ru}+^{96}\text{Ru}$ and 1.9 billion $^{96}\text{Zr}+^{96}\text{Zr}$ collisions at $\sqrt{s_{NN}} = 200$ GeV, collected in 2018. The two systems were combined to maximize statistical precision.
• Reconstruction:
  • Charmonia were reconstructed via their decay into electron-positron pairs ($e^+e^-$) at mid-rapidity ($|y| < 1$).
  • Electron Identification: Utilized the Time Projection Chamber (TPC) for ionization energy loss ($n\sigma_e$), Time Of Flight (TOF) for velocity ($\beta$), and the Barrel Electromagnetic Calorimeter (BEMC) for energy-to-momentum ratio ($E/p$).
  • Machine Learning: An XGBoost (eXtreme Gradient Boosting) algorithm was employed to enhance signal significance. A Boosted Decision Tree (BDT) was trained on simulated signal events and background data (sidebands in invariant mass) to distinguish charmonium signals from combinatorial background. A default BDT threshold of 0.7 was selected to optimize significance.
• Signal Extraction:
  • Invariant mass spectra were fitted using a Crystal-Ball function (for the signal) and a linear function (for residual background from heavy-flavor decays and Drell-Yan processes).
  • Raw yields were corrected for reconstruction efficiency and acceptance.
• Analysis Variables:
  • Double Ratio: Defined as $\frac{(\psi(2S)/J/\psi)_{AA}}{(\psi(2S)/J/\psi)_{pp}}$. This cancels many systematic uncertainties and isolates the medium effects.
  • Centrality: Classified based on charged particle multiplicity (0–80% centrality range).
  • Transverse Momentum ($p_T$): Analyzed in bins to study kinematic dependence.
• Reference Values: The $p+p$ reference ratio was interpolated from world data at 200 GeV. Cold Nuclear Matter (CNM) effects were estimated by interpolating $p+Au$ data, serving as an upper limit for non-QGP suppression.

3. Key Contributions

• First Measurement at 200 GeV in Small Systems: This is the first measurement of inclusive $\psi(2S)$ and $J/\psi$ production in Ru+Ru and Zr+Zr collisions at RHIC energies, bridging the gap between low-energy (SPS) and high-energy (LHC) results.
• Advanced Signal Extraction: The application of supervised machine learning (XGBoost) to charmonium reconstruction in heavy-ion collisions significantly improved the signal-to-background ratio, allowing for precise measurements in high-multiplicity environments.
• Quantification of Sequential Suppression: The study provides a rigorous quantitative test of the sequential suppression hypothesis in a regime where regeneration effects are expected to be significant but potentially different from LHC energies.

4. Key Results

• Sequential Suppression Observed: The inclusive double ratio of $\psi(2S)$ to $J/\psi$ in the 0–80% centrality class was measured to be:
  $$0.41 \pm 0.10 \text{ (stat)} \pm 0.03 \text{ (syst)} \pm 0.02 \text{ (ref)}$$
  This value is significantly lower than unity, deviating by 5.6 standard deviations. This confirms that $\psi(2S)$ is significantly more suppressed than $J/\psi$ in these collisions.
• Centrality Dependence: There is a hint of a decreasing trend in the double ratio from peripheral (0–80%) to central (0–20%) collisions, consistent with the expectation that QGP effects (dissociation) increase with the size of the overlap region. However, the statistical significance of this trend is limited.
• Transverse Momentum Dependence: The double ratio shows no significant dependence on transverse momentum ($p_T$) in the range $0.2 < p_T < 4.0$ GeV/c.
• Comparison with Models and CNM:
  • The measured double ratio is lower than the interpolated value for $p+Au$ collisions ($\approx 0.79$), suggesting that the suppression observed is due to hot medium (QGP) effects beyond just Cold Nuclear Matter effects.
  • The Tsinghua transport model (incorporating continuous dissociation and regeneration) agrees well with the data.
  • The Statistical Hadronization Model (SHMc), which assumes complete dissociation and regeneration at hadronization, also shows reasonable agreement, though it predicts no energy dependence.
• $p_T$ Differential: In the low $p_T$ region ($0.2–2.0$GeV/c), the ratio in heavy-ion collisions is significantly lower than in$p+p$collisions (4.1$\sigma$ difference).

5. Significance

• Evidence for QGP Formation: The observation of strong sequential suppression ($\psi(2S) \ll J/\psi$) in Ru+Ru and Zr+Zr collisions at 200 GeV provides robust evidence for the formation of a hot, deconfined medium even in smaller collision systems and at intermediate energies.
• Constraints on QGP Dynamics: The results constrain the space-time evolution of the QGP. The lack of strong $p_T$ dependence and the specific magnitude of the suppression help refine theoretical models regarding the balance between charmonium dissociation and regeneration.
• System Size Scaling: By comparing these results with Pb+Pb data, the study helps elucidate how the size of the colliding nuclei influences the QGP properties and the survival probability of different quarkonium states.
• Methodological Benchmark: The successful use of machine learning for signal extraction in high-multiplicity heavy-ion collisions sets a precedent for future analyses of rare probes in similar environments.

In conclusion, the STAR Collaboration has provided definitive experimental evidence that $\psi(2S)$ mesons are more strongly suppressed than $J/\psi$ mesons in heavy-ion collisions at RHIC, validating the concept of sequential suppression and offering new constraints on the transport properties of the Quark-Gluon Plasma.