Measurement of inclusive $J/\psi$ polarization in Ru+Ru and Zr+Zr collisions at $\sqrt{s_{\rm NN}}=200$ GeV at STAR

The STAR experiment at RHIC presents the first measurement of inclusive $J/\psi$ polarization in Ru+Ru and Zr+Zr collisions at $\sqrt{s_{\rm NN}}=200$ GeV, finding that the polarization parameters are consistent with zero across various transverse momenta and collision centralities, aligning with previous $p+p$ measurements and transport-model calculations.

The Gist

The Big Picture: A Cosmic Soup and a Tiny Magnet

Imagine smashing two heavy atoms (like Ruthenium or Zirconium) together at nearly the speed of light. When they collide, they create a tiny, super-hot drop of "primordial soup" called the Quark-Gluon Plasma (QGP). In this soup, the usual rules of physics are suspended: particles that are normally glued together (quarks) float around freely.

Scientists want to know: How does this soup affect the particles moving through it?

To find out, they use a specific particle called the J/ψ meson as a probe. Think of the J/ψ as a tiny, spinning top made of a charm quark and an anti-charm quark. Because it's so small and heavy, it's like a messenger that survives the explosion and flies out to tell us what happened inside the soup.

The Mystery: Is the Top Spinning?

The main question of this paper is about polarization. In simple terms, polarization asks: Is the J/ψ meson spinning in a specific direction, or is it spinning randomly?

• If it's polarized: The tops are all leaning the same way (like a field of wheat blowing in the wind).
• If it's unpolarized: The tops are spinning in every direction randomly (like a bowl of tossed salad).

Scientists have two main theories about what happens in the QGP:

1. The "Melting" Theory: The hot soup might melt the J/ψs. If only the ones spinning a certain way survive, we should see a strong pattern (polarization).
2. The "Rebirth" Theory: Sometimes, the soup is so full of floating quarks that they randomly bump into each other and form new J/ψs. Since these are formed by accident, they should have no preferred spinning direction (unpolarized).

The Experiment: The STAR Detector as a Giant Camera

The STAR experiment at the Relativistic Heavy Ion Collider (RHIC) is like a massive, 360-degree camera surrounding the collision point.

1. The Collision: They smashed together Ru+Ru and Zr+Zr atoms (two different types of heavy metals) at 200 GeV of energy. They chose these two because they are very similar, allowing them to combine the data for better statistics.
2. The Catch: The J/ψ meson is unstable. It almost instantly breaks apart into an electron and a positron (like a firecracker splitting into two sparks). The camera doesn't see the J/ψ directly; it sees these two sparks flying out.
3. The Filter: The detector has to be very picky. It has to ignore billions of other particles (like pions and protons) and only keep the electron/positron pairs that look like they came from a J/ψ. It's like trying to find two specific red marbles in a bucket of a billion mixed marbles.

The Method: Checking the Angles

Once they found the J/ψ candidates, the scientists looked at the angles at which the electron and positron flew out.

• Imagine the J/ψ is a spinning top. If it's spinning horizontally, the sparks fly out sideways. If it's spinning vertically, they fly out up and down.
• The scientists measured these angles in two different "reference frames" (two different ways of looking at the collision):
  1. The Helicity Frame: Looking from the perspective of the collision's forward motion.
  2. The Collins-Soper Frame: Looking from the perspective of the colliding beams.

They did this for different collision "strengths" (centrality) and different speeds (transverse momentum).

The Results: The "Flat" Surprise

After crunching the numbers, the result was surprisingly boring (in a good scientific way):

The J/ψ mesons were completely unpolarized.

• The Analogy: Imagine throwing a million spinning tops into a room. If you check them all later, you find they are pointing in every single direction with equal probability. There is no pattern.
• The Numbers: The polarization parameters (which measure how "leaning" the tops are) were consistent with zero. Whether the J/ψ was moving fast or slow, or whether the collision was a glancing blow or a head-on smash, the result was the same: No preferred direction.

What Does This Mean?

1. It matches the "Rebirth" idea: The fact that the J/ψs are unpolarized suggests that many of them might be "regenerated" (reborn) inside the soup. Since they are formed randomly from the soup's ingredients, they don't inherit any specific spin direction.
2. It matches the "Reference" data: This result is exactly the same as what they see in simple proton-proton collisions (where no soup is formed). This suggests that even in the heavy-ion collisions, the complex mix of "original" J/ψs and "newly born" J/ψs averages out to zero polarization.
3. It rules out some theories: Some theories predicted that the QGP would strip away the "wrong" spins, leaving only a polarized group. This experiment says, "Nope, that didn't happen."

The Takeaway

The STAR collaboration took a huge sample of heavy-ion collisions, filtered out the noise, and measured the spin of the J/ψ mesons. They found that the Quark-Gluon Plasma does not seem to align the spins of these particles.

It's like walking into a room where you expected everyone to be marching in step, but instead, everyone is dancing to their own beat. This helps physicists refine their models of how the universe's "primordial soup" behaves, confirming that the creation of these particles inside the soup is a chaotic, random process rather than an orderly one.

Technical Summary

1. Problem Statement and Motivation

The Quark-Gluon Plasma (QGP), a deconfined state of matter, is studied using heavy-ion collisions. The $J/\psi$ meson (a charm-anticharm bound state) is a primary probe for QGP properties due to its sensitivity to dissociation (melting) and regeneration (recombination) mechanisms. However, interpreting $J/\psi$ yields is complicated by the mixture of production sources:

• Primordial: Prompt production and feed-down from excited charmonia ($\psi(2S)$, $\chi_{cJ}$) or $b$-hadrons.
• Regenerated: Recombination of deconfined $c\bar{c}$ pairs in the medium.

While $J/\psi$ yields have been extensively measured, $J/\psi$ polarization (the alignment of the spin vector) offers a new observable to disentangle these mechanisms. Different production channels and medium effects (e.g., color screening, vorticity) predict distinct polarization signatures. Prior to this work, $J/\psi$ polarization had only been measured at the LHC (forward rapidity, $\sqrt{s_{NN}} = 5.02$ TeV). There was a critical gap in data at mid-rapidity and RHIC energies ($\sqrt{s_{NN}} = 200$ GeV), where regeneration contributions are smaller and non-prompt contributions from $b$-hadrons are negligible. This paper addresses the first measurement of inclusive $J/\psi$ polarization in heavy-ion collisions at RHIC.

2. Methodology

Dataset and Experimental Setup

• Collisions: The analysis uses data from Ru+Ru and Zr+Zr collisions at $\sqrt{s_{NN}} = 200$ GeV collected by the STAR experiment at RHIC.
• Sample Size: Approximately $2 \times 10^9$ minimum-bias events for each system, combined to enhance statistical precision due to their similar nuclear structures.
• Detector: The analysis utilizes the Time Projection Chamber (TPC) for tracking and $dE/dx$, the Time-of-Flight (TOF) detector for velocity, and the Barrel Electromagnetic Calorimeter (BEMC) for energy deposition.
• Kinematics: Measurements are performed at mid-rapidity ($|y_{J/\psi}| < 0.8$) and transverse momentum ($0.2 < p_T < 10$ GeV/c) across collision centralities (0–80%).

Event Selection and Reconstruction

• Trigger: Minimum bias trigger requiring coincidence in Zero Degree Calorimeters (ZDC).
• Track Selection: Tracks must originate from the primary vertex ($|v_z| < 35$ cm), have $p_T \ge 0.2$ GeV/c, and satisfy quality cuts (e.g., $n_{HitsFit} \ge 20$, $DCA < 1$ cm).
• Electron Identification: A multi-variable approach is used to identify electrons ($e^\pm$) and reject hadrons:
  • TPC: $n\sigma_e$ (deviation of measured $dE/dx$ from electron expectation).
  • TOF: Velocity cut ($|1 - 1/\beta| < 0.025$) for low $p_T$.
  • BEMC: Energy-to-momentum ratio ($0.5 < E/p < 1.5$) for high $p_T$.
  • Specific cut combinations are applied based on $p_T$ ranges and detector matching scenarios (TOF only, BEMC only, or both).
• Signal Extraction: $J/\psi$ candidates are reconstructed via the $e^+e^-$ decay channel. The invariant mass spectrum is fitted using a Crystal-Ball function for the signal and a mixed-event technique (normalized in sidebands) plus a polynomial for the background.

Polarization Analysis

• Frames: Polarization is measured in two reference frames:
  1. Helicity (HX) Frame: $z$-axis along the $J/\psi$ momentum in the CM frame (sensitive to final-state hadronization).
  2. Collins-Soper (CS) Frame: $z$-axis bisecting the angle between beam directions (sensitive to initial-state partonic kinematics).
• Parameters: The angular distribution $W(\theta, \phi)$ is described by polarization parameters $\lambda_\theta$, $\lambda_\phi$, and $\lambda_{\theta\phi}$. The analysis extracts $\lambda_\theta$ and $\lambda_\phi$ by fitting the 1D distributions of $\cos\theta$ and $\phi$.
• Efficiency Correction: A Toy Monte Carlo (ToyMC) simulation is employed to correct for detector acceptance and efficiency ($A \times \epsilon$). An iterative procedure is used:
  1. Assume unpolarized $J/\psi$ to generate initial efficiency maps.
  2. Extract polarization parameters.
  3. Feed parameters back into the simulation.
  4. Repeat until convergence (typically 3–5 iterations).
• Systematics: Uncertainties are evaluated for signal extraction (fit ranges, background models), tracking efficiency (varying quality cuts), and electron identification (comparing data-driven methods with simulations).

3. Key Contributions

• First Measurement at RHIC: This is the first measurement of inclusive $J/\psi$ polarization in heavy-ion collisions at $\sqrt{s_{NN}} = 200$ GeV.
• Isotopic Collision Systems: Utilization of Ru+Ru and Zr+Zr collisions allows for high-statistics studies of isobaric systems, minimizing nuclear structure differences while maximizing statistical power.
• Frame Invariance Check: The study provides a rigorous check of frame invariance ($\lambda_{inv}$) at RHIC energies, confirming consistency between the HX and CS frames.
• Model Comparison: The results are compared with the Tsinghua (THU) transport model, which accounts for both dissociation and regeneration, providing a benchmark for theoretical descriptions of $J/\psi$ dynamics at RHIC.

4. Results

• Polarization Parameters: The measured parameters $\lambda_\theta$ and $\lambda_\phi$ are consistent with zero across the entire measured $p_T$ range ($0.2 - 10$ GeV/c) and all centrality classes (0–80%) in both the HX and CS frames.
• Frame Invariance: The frame-invariant parameter $\lambda_{inv}$ is also consistent with zero and shows agreement between the two reference frames, validating the measurement robustness.
• Comparison with Theory and Data:
  • The results are consistent with previous $p+p$ measurements at 200 GeV.
  • The data are well-described by the THU transport model, which assumes regenerated $J/\psi$ are unpolarized and primordial $J/\psi$ follow perturbative QCD expectations.
• Regeneration Fraction: A fit assuming a mixture of primordial and regenerated $J/\psi$ suggests that if primordial $J/\psi$ are unpolarized, the regenerated component is also likely unpolarized. However, current precision is insufficient to definitively separate the contributions or detect small deviations caused by feed-down suppression (e.g., from $\chi_{cJ}$).

5. Significance

• Validation of Transport Models: The agreement with the THU model supports the current understanding that at RHIC energies, the regeneration contribution to inclusive $J/\psi$ is modest and does not dominate the polarization signal, unlike at LHC energies where regeneration is more significant.
• Baseline for Future Studies: Establishing that $J/\psi$ polarization is consistent with zero in heavy-ion collisions at 200 GeV provides a crucial baseline. Future measurements with higher precision (e.g., at the Electron-Ion Collider or with upgraded detectors) can look for subtle deviations that might reveal:
  • Specific medium-induced spin alignment (e.g., via vorticity or electromagnetic fields).
  • Detailed changes in feed-down fractions ($\chi_{cJ}$ vs. direct $J/\psi$) due to QGP suppression.
• Methodological Advancement: The successful application of the iterative efficiency correction and the combination of isobaric collision data demonstrate a robust methodology for polarization measurements in high-multiplicity environments.

In conclusion, this paper establishes that inclusive $J/\psi$ mesons produced in 200 GeV Ru+Ru and Zr+Zr collisions exhibit no significant polarization, consistent with zero and with transport model predictions, thereby refining our understanding of charmonium production mechanisms in the QGP at RHIC energies.