Charmonium production in low energy nuclear collisions at SPS and FAIR: achievements $\&$ prospects

This paper reviews the current status and theoretical understanding of charmonium production in low-energy nuclear collisions at SPS, Fermilab, and HERA facilities, while outlining future prospects for measurements near the kinematic threshold in the upcoming CBM and NA60+ experiments.

The Gist

Imagine the universe as a giant kitchen where the ingredients are tiny particles called quarks and gluons. Under normal conditions, these ingredients are stuck together in little bundles (like protons and neutrons). But if you turn up the heat and squeeze them together hard enough, they melt into a super-hot, super-dense soup called the Quark-Gluon Plasma (QGP). Scientists want to study this soup to understand how the universe worked right after the Big Bang.

One of the best ways to check if this soup exists is to look for a specific "ingredient" called Charmonium. Think of Charmonium as a very delicate, rare pair of twins (a charm quark and an anti-charm quark) that usually stick together tightly.

Here is the story of what this paper says about finding these twins in different types of particle collisions:

1. The "Melting Pot" Theory

In the 1980s, scientists predicted that if you create this hot QGP soup, the heat will be so intense that it acts like a giant magnet shield. This shield would push the twin charm particles apart, preventing them from sticking together. If the twins melt, you see fewer of them. This is called "suppression."

• The Analogy: Imagine trying to hold hands with a friend in a crowded, hot room. If the room gets too hot and crowded (the QGP), you might be forced to let go.
• The Twist: There are different types of twins. Some are holding hands very tightly (like the J/ψ particle), while others are holding hands loosely (like the ψ(2S) particle). The theory says the loose ones should let go (melt) at lower temperatures, while the tight ones need more heat. This is called sequential suppression.

2. The Problem: The "Cold" Noise

Before scientists could say, "Aha! The twins melted because of the hot soup!", they had to rule out other reasons why the twins might disappear.

Even in "cold" collisions (where no hot soup is made), the twins can get knocked apart just by bumping into other particles in the target material. This is called Cold Nuclear Matter (CNM) effect.

• The Analogy: Imagine you are trying to count how many people drop their ice cream because of a heatwave. But, people also drop ice cream because they trip on the sidewalk. You have to know exactly how many people trip on the sidewalk (the cold effect) before you can blame the heatwave (the hot soup).

The paper reviews decades of experiments (mostly at CERN's SPS facility) that tried to measure this "sidewalk tripping" in simple collisions (proton hitting a nucleus) to create a baseline. They found that the "tripping" gets worse as the target gets bigger and the energy gets lower.

3. What We Know So Far (The High-Energy Results)

At very high energies (like at the LHC or RHIC), scientists saw that the twins did disappear more than expected from just "tripping." However, there was a catch: at these super-high energies, the twins can also re-form. It's like if the twins melt, but because there are so many loose ingredients floating around, they accidentally bump into each other and hold hands again. This "reformation" hides the melting effect, making the data complicated.

4. The New Frontier: Low Energy Collisions

This paper focuses on the low-energy collisions happening at facilities like CERN-SPS and the upcoming FAIR facility in Germany. Why go lower?

• Less Reformation: At lower energies, there aren't enough loose ingredients floating around to re-form the twins. If the twins disappear, it's almost certainly because they melted or were knocked apart, not because they re-formed.
• The Threshold: The FAIR facility will be able to smash particles together at energies so low that making these twins should be impossible according to simple rules (like trying to bake a cake without enough flour). However, the paper notes that theoretical models suggest that if you smash the particles together fast enough and often enough, they might "borrow" energy from multiple bumps to still make the twins. Finding these "impossible" twins would tell us a lot about how matter behaves under extreme pressure.

5. The Future: New Experiments

The paper highlights two upcoming experiments designed to solve these mysteries:

• NA60+ (at CERN): This will act like a high-speed camera, smashing protons and heavy ions together at various low energies. It will measure exactly how many twins disappear in "cold" collisions to create a perfect baseline, and then check heavy-ion collisions to see if the "hot soup" causes extra melting.
• CBM (at FAIR): This is the heavy hitter. It will smash heavy ions together at the lowest possible energies, right at the edge where making twins should be impossible. It is designed to handle a massive amount of data (like a super-fast highway toll booth) to catch these rare events.

Summary

The paper is a roadmap for the next generation of particle physics. It says:

1. We know how to spot the "hot soup" (QGP) by seeing if rare particle twins melt.
2. We have spent years measuring the "cold noise" (normal nuclear effects) to make sure we aren't fooling ourselves.
3. Now, we are moving to lower energies where the "re-formation" trick stops working, giving us a clearer picture of the melting process.
4. New, powerful experiments (NA60+ and CBM) are being built to catch these rare events, even at energies where they theoretically shouldn't exist, to help us map out the secrets of the universe's most extreme states of matter.

Technical Summary

Technical Summary: Charmonium Production in Low Energy Nuclear Collisions at SPS and FAIR

Problem Statement
The primary objective of relativistic heavy-ion collision experiments is to characterize the Quark-Gluon Plasma (QGP) and map the Quantum Chromodynamics (QCD) phase diagram, particularly in the region of high net baryon density ($\mu_B$) and moderate temperature ($T$). While high-energy facilities (RHIC, LHC) have extensively studied the low-$\mu_B$ regime, the high-$\mu_B$ region remains less explored due to theoretical challenges (e.g., the fermionic sign problem in lattice QCD) and experimental limitations. Charmonium ($c\bar{c}$ bound states), specifically the $J/\psi$ and $\psi(2S)$ mesons, serve as critical probes for deconfinement. The Matsui-Satz hypothesis posits that color screening in a deconfined medium leads to the sequential melting of charmonium states. However, interpreting suppression patterns in heavy-ion (A+A) collisions requires disentangling "anomalous" suppression (due to QGP) from "normal" nuclear suppression caused by Cold Nuclear Matter (CNM) effects (e.g., nuclear parton distribution modifications, initial/final state energy loss, and absorption).

Currently, there is a scarcity of experimental data on charmonium production at collision energies below the top SPS energy ($\sqrt{s_{NN}} \approx 17.3$ GeV). At these lower energies, the interplay between CNM effects and potential QGP signatures is complex. Furthermore, theoretical models predict that at very low energies (near or below the kinematic threshold for $c\bar{c}$ production), sub-threshold charm production may occur via multi-step nucleon interactions, and the regeneration of charmonium via recombination is expected to be negligible. This lack of data hinders the precise quantification of CNM baselines and the identification of the onset of deconfinement in high-$\mu_B$ matter.

Methodology and Scope
This article reviews the status of charmonium production in low-energy fixed-target proton-nucleus (p-A) and nucleus-nucleus (A-A) collisions, synthesizing results from CERN-SPS, Fermilab, and HERA facilities. The review focuses on:

1. Experimental History: A detailed analysis of data from NA38, NA50, and NA60 collaborations at CERN-SPS, covering systems from p+p and p+A to O+U, S+U, In+In, and Pb+Pb.
2. Theoretical Frameworks: An examination of production models (Color Evaporation Model, Color Singlet Model, NRQCD) and suppression mechanisms (Debye screening, statistical hadronization, transport models, and open quantum systems).
3. CNM Effects: A critical assessment of "normal" nuclear suppression, quantified via the nuclear modification factor ($R_{AA}$) and absorption cross-sections ($\sigma_{abs}$), and the energy dependence of these effects.
4. Future Prospects: An investigation of the physics potential of upcoming experiments: NA60+ at CERN-SPS and the Compressed Baryonic Matter (CBM) experiment at FAIR SIS100.

The paper utilizes simulation results and physics performance studies to evaluate the feasibility of measuring charmonium in the low-energy regime, specifically addressing the challenges of low production cross-sections and high interaction rates.

Key Contributions and Results

• Review of SPS Results:

  • p+A Collisions: Data from NA38, NA50, and NA60 confirm that charmonium production in p+A collisions is suppressed relative to p+p collisions. This suppression increases with the target mass number ($A$) and is stronger at lower beam energies. The suppression is parameterized by an effective absorption cross-section ($\sigma_{eff}^{abs}$), which ranges from $\sim 4.2$ mb at 450 GeV to $\sim 7.6$ mb at 158 GeV. The $\psi(2S)$ state exhibits stronger suppression than $J/\psi$ due to its weaker binding energy.
  • A+A Collisions: In Pb+Pb collisions at 158 A GeV, NA50 observed "anomalous" suppression of $J/\psi$ beyond the expected CNM effects, particularly in central collisions. The $\psi(2S)$ showed even stronger suppression, hinting at sequential melting. However, the interpretation remains debated, with models invoking both QGP formation and hadronic comover interactions capable of describing the data.
  • Kinematic Observables: Measurements of transverse momentum ($p_T$) broadening, elliptic flow ($v_2$), and polarization provide additional constraints. At SPS energies, $J/\psi$ $v_2$ was found to be non-zero, suggesting some degree of interaction with the medium, though regeneration is negligible.

• Theoretical Insights for Low Energies:

  • Regeneration: At SPS and FAIR energies, the number of $c\bar{c}$ pairs per event is very low ($N_{c\bar{c}} \approx 0.2$ at top SPS), making exogamous recombination (formation from distinct pairs) effectively impossible. Regeneration is limited to endogamous recombination (recombination of the original pair), resulting in a very low overall regeneration probability compared to RHIC/LHC.
  • Sub-threshold Production: Theoretical models (e.g., UrQMD) predict that at FAIR SIS100 energies ($\sqrt{s_{NN}} < 4.9$ GeV), where elementary $p+p \to J/\psi + X$ is kinematically forbidden, charmonium can still be produced via multi-step baryonic collisions (e.g., $N^* \to J/\psi + N$). This production is sensitive to the Equation of State (EoS) of dense baryonic matter.
  • CNM Baseline: The paper emphasizes that CNM effects (nuclear absorption, shadowing) are expected to be amplified at lower energies, making a precise measurement of p+A collisions essential to establish a baseline for A+A studies.

• Prospects for NA60+ and CBM:

  • NA60+ (SPS): Plans to measure $J/\psi$ in p+A and Pb+Pb collisions down to $\sqrt{s_{NN}} \approx 8.8$ GeV (40 A GeV beam). Simulations indicate that with the upgraded vertex telescope and muon spectrometer, the experiment can detect $\sim 20\%$ anomalous suppression in central Pb+Pb collisions. It also aims to probe intrinsic charm components in the nucleon wave function.
  • CBM (FAIR SIS100): Designed to operate at interaction rates up to 10 MHz, CBM aims to measure sub-threshold $J/\psi$ production in Au+Au collisions and p+A collisions. Simulations suggest that despite the extremely low cross-sections ($\sim 5 \times 10^{-6}$ per event), the high luminosity and optimized detector setup (Silicon Tracking System, Muon Chambers) will allow for statistically significant measurements. These measurements will probe the EoS of dense matter and the in-medium properties of charmed hadrons.

Significance and Claims
The paper argues that the upcoming measurements by NA60+ and CBM are critical for addressing open questions in the QCD phase diagram that cannot be resolved at higher energies. Specifically:

1. Baseline Calibration: Precise measurements of p+A collisions at low energies are necessary to disentangle CNM effects from potential QGP signals in A+A collisions, as the magnitude of CNM suppression is energy-dependent.
2. Threshold Determination: A beam energy scan of $J/\psi$ suppression could experimentally identify the threshold energy (or temperature) at which anomalous suppression (melting) begins, providing a direct test of Lattice QCD predictions for melting temperatures.
3. Sub-threshold Physics: The observation of charmonium production below the kinematic threshold at FAIR would provide a novel probe of the high-density EoS and multi-step reaction mechanisms in nuclear matter.
4. Intrinsic Charm and Resonance Interactions: Low-energy p+A measurements offer a unique opportunity to study intrinsic charm contributions and resonance-nucleon interaction cross-sections, which are poorly constrained by current data.

The authors conclude that while the extremely small charm production cross-sections present a significant experimental challenge, the high-intensity beams and advanced detector technologies of NA60+ and CBM make these measurements feasible. These efforts are essential for a coherent understanding of charmonium dynamics in the high-$\mu_B$ regime of the QCD phase diagram.