Measurement of di-muons from 400 GeV/c protons interacting in a thick molybdenum/tungsten target

This paper reports the measurement of $J/\psi$ production cross-sections from 400 GeV/c protons interacting in a thick molybdenum/tungsten target, finding results consistent with Monte Carlo simulations and the NA50 experiment while observing no significant enhancement from secondary production or cascade collisions within the target.

The Gist

The Big Picture: A "Crash Test" for a Future Experiment

Imagine the SHiP experiment is a massive, high-tech fortress being built to hunt for invisible, ghost-like particles (like Axions). To protect the sensitive detectors inside from being blinded by a flood of regular particles, the scientists need to build a giant muon shield (a magnetic wall).

But before they build the wall, they need to know exactly how much "traffic" (muons) they are expecting. If they underestimate the traffic, the shield won't work, and the experiment will fail.

To test this, the team built a replica of the target (the thing the beam hits) and fired a beam of protons (tiny, fast bullets) at it. They didn't just count the muons; they looked specifically for a very specific type of "traffic jam" caused by a particle called the J/ψ (J-psi).

The Analogy: The Bowling Alley and the Mystery Balls

Think of the experiment like a giant, high-speed bowling alley:

1. The Bowler: A beam of protons traveling at nearly the speed of light (400 GeV).
2. The Pins: A thick, heavy target made of Molybdenum and Tungsten (about 1.5 meters long). This is much thicker than the targets used in previous experiments.
3. The Collision: When the protons hit the pins, they shatter, creating a shower of new particles.
4. The Mystery Balls (J/ψ): Among the debris, some heavy particles called J/ψ mesons are created. These are unstable and almost immediately break apart into two muons (which are like heavy electrons).
5. The Goal: The scientists want to count how many of these "Mystery Ball" pairs are created. Why? Because these pairs are the "troublemakers" that the muon shield needs to block.

The Investigation: Finding the Signal in the Noise

The scientists had two main challenges:

1. The "Thick Target" Problem
Previous experiments (like NA50) used very thin targets (like a sheet of paper). This paper used a target as thick as a small room (1.5 meters).

• The Fear: When a particle hits a thick wall, it doesn't just bounce once. It might hit, create a new particle, that new particle hits again, and creates another one. This is called a cascade.
• The Question: Did the thick target create extra J/ψ particles through these secondary collisions, or was the production rate the same as in thin targets?

2. The "Blurry Camera" Problem
The muons had to travel through 1.5 meters of target material and 2.4 meters of iron before reaching the detector.

• The Issue: As they traveled, they lost energy (like a runner getting tired) and bounced around randomly (like a pinball hitting bumpers). This made it hard to know exactly how fast they were going or where they came from.
• The Fix: The team used a computer simulation (a "digital twin" of the experiment) to correct for this. They essentially said, "Okay, the ball looked like it was going 50 mph, but because it hit 10 bumpers, it was actually going 60 mph." They applied these corrections to get a clear picture.

The Results: What Did They Find?

After cleaning up the data and correcting for the "blur," here is what they discovered:

• The Signal is Real: They found a clear "bump" in the data at the exact mass where J/ψ particles should be. It's like finding a specific type of coin in a pile of gravel.
• No Surprise Boost: They compared their results to the older, thinner-target experiments (NA50).
  • Old Result: ~0.99 units of production.
  • New Result: ~1.18 units of production.
  • Conclusion: The numbers are very close. The "thick wall" did not create a massive explosion of extra J/ψ particles. The secondary collisions (the cascade) contributed less than 32% (likely much less).
• The Simulation Works: Their computer models (using software called Pythia) predicted the results reasonably well, though they had to tweak the models slightly to match the real-world data perfectly.

Why Does This Matter?

1. Building the Shield: Since the production rate of these "troublemaker" muons is now well-understood, the engineers can design the magnetic shield for the SHiP experiment with confidence. They know exactly how strong the magnets need to be to stop the noise.
2. Validating Physics: It confirms that our current understanding of how heavy particles are made in collisions holds up, even when the target is very thick.
3. Future Searches: By understanding this "background noise" so well, the SHiP experiment will be better at spotting the real ghosts (new physics) when they finally turn the machine on.

The Bottom Line

The SHiP team fired a super-fast beam into a thick block of metal to see how many "mystery particle pairs" were created. They found that even in a thick block, the production rate is predictable and doesn't explode unexpectedly. This gives them the green light to build their massive magnetic shield and start hunting for the new physics that could change our understanding of the universe.

Technical Summary

1. Problem Statement and Motivation

The SHiP (Search for Hidden Particles) experiment at CERN aims to detect rare physics phenomena, such as heavy neutral leptons. A critical component of the experiment's design is the muon shield, which must effectively suppress the background of high-momentum muons produced in the primary proton-target interaction to prevent them from mimicking signal events.

• The Challenge: $J/\psi$ mesons produced in proton-nucleus collisions decay into di-muons ($J/\psi \to \mu^+\mu^-$). These muons possess high transverse momentum ($p_T$) and constitute a significant source of background.
• The Gap: Previous measurements (e.g., by the NA50 experiment) were performed using thin targets (effective interaction lengths $L_{eff}/\lambda_{int} \approx 0.38$). The SHiP experiment utilizes a thick target (1.5 m long, $\approx 13$ interaction lengths). In such thick targets, secondary interactions (cascade collisions) of particles produced in the primary interaction can generate additional $J/\psi$ mesons.
• Objective: To measure the $J/\psi$ production cross-section in a thick target replica to validate Monte Carlo (MC) simulations, quantify potential enhancements due to secondary production, and refine the design of the muon shield.

2. Methodology

Experimental Setup

• Beam: 400 GeV/c protons from the CERN SPS.
• Target: A 1.5 m long target composed of Molybdenum/Tungsten (replica of the SHiP target), followed by a 2.4 m iron hadron absorber.
• Detector: A spectrometer consisting of four drift-tube tracker stations, a magnet, and a muon tagger made of Resistive Plate Chambers (RPCs).
• Data: Collected in 2018, focusing on events with two or more reconstructed tracks.

Data Analysis and Reconstruction

1. Track Selection: Events were selected with two tracks having momenta between 20 GeV/c and 300 GeV/c.
2. Corrections:
   • Energy Loss: Muons lose significant energy (average ~10 GeV) traversing the target and absorber. Corrections were applied based on Geant4 simulations.
   • Multiple Scattering: The direction of reconstructed tracks was corrected by replacing the fitted momentum direction with the vector defined by the target center and the first measured hit. This significantly improved the resolution of the invariant mass and kinematic variables.
3. Signal Extraction:
   • The di-muon invariant mass distribution was fitted using Bukin functions (preferred over Crystal Ball functions for better tail description) to separate the $J/\psi$ signal from low-mass resonances ($\eta, \omega, \rho^0, \phi$) and background.
   • A free normalization for $\psi(2S)$ was included, yielding an upper limit of < 2.1% for its contribution.
4. Monte Carlo Simulation:
   • Pythia v8: Used for primary interactions and minimum bias events.
   • Pythia v6: Used specifically to model heavy flavor production in secondary (cascade) interactions within the thick target.
   • Reweighting: To match data, Pythia v6 rapidity distributions were reweighted to Pythia v8, and Pythia v8 $p_T$ distributions were reweighted to Pythia v6, acknowledging discrepancies between generators.

Cross-Section Calculation

The differential cross-section was calculated by:
$$\frac{d\sigma}{dy} = \frac{N_{yield}}{A \times \epsilon \times \mathcal{L} \times B_{\mu\mu}}$$
Where $N_{yield}$ is the fitted signal yield, $A$ is geometric acceptance, $\epsilon$ is reconstruction efficiency, $\mathcal{L}$ is integrated luminosity, and $B_{\mu\mu}$ is the branching ratio. Migration effects between true and reconstructed rapidity were corrected using MC-derived response matrices.

3. Key Contributions

• First Thick-Target Measurement: Provided the first direct measurement of $J/\psi$ production in a target with an interaction length of ~13, allowing for the study of cascade effects previously unmeasured.
• Validation of Simulation: Demonstrated that while Pythia v8 describes the $p_T$ spectrum well, Pythia v6 is required to describe the rapidity distribution in this specific kinematic regime.
• Systematic Correction Techniques: Developed and validated robust methods for correcting energy loss and multiple scattering in a high-density environment, improving the invariant mass resolution from $\sim 0.15$ to $\sim 0.10$ in $\cos\Theta_{CS}$ and significantly sharpening the mass peak.
• Polarization Study: Measured the $J/\psi$ polarization parameter $\Lambda$ in the Collins-Soper frame, finding no significant polarization ($\Lambda = 0.11 \pm 0.14$).

4. Results

• Production Cross-Section:
  In the rapidity interval $0.3 < y_{cm} < 0.6$ (maximizing overlap with NA50), the measured cross-section per nucleon is:
  $$B_{\mu^+\mu^-}\sigma(J/\psi)/A = (1.18 \pm 0.04_{stat} \pm 0.10_{syst}) \text{ nb/nucleon}$$
  This is compared to the NA50 extrapolated result (for thin targets):
  $$B_{\mu^+\mu^-}\sigma(J/\psi)/A = (0.99 \pm 0.04) \text{ nb/nucleon}$$

• Secondary Production (Cascade) Limits:
  The difference between the thick-target measurement and the thin-target extrapolation is within systematic uncertainties.

  • Conclusion: No significant enhancement due to secondary $J/\psi$ production inside the target was observed.
  • Upper Limit: The contribution from cascade collisions is constrained to be < 32%.

• Kinematic Distributions:

  • The $J/\psi$ signal was observed up to high rapidities ($y_{cm} \approx 2.0$).
  • The transverse momentum ($p_T$) distribution is harder than predicted by Pythia v8 primary-only simulations but is well-described by the reweighted models.

5. Significance

• SHiP Experiment Design: The results confirm that the rate of high-$p_T$ muons from $J/\psi$ decays in the thick SHiP target is consistent with current simulation models (Pythia). This validates the design of the muon shield, ensuring it will effectively suppress background without being over-engineered.
• Physics Constraints: The lack of significant secondary production enhancement suggests that cascade interactions in heavy nuclei at 400 GeV do not drastically alter the $J/\psi$ yield compared to primary interactions, refining our understanding of heavy flavor production in dense matter.
• Future Applications: The methodology for handling low invariant mass combinations and correcting for energy loss in thick targets provides a template for future searches for Axion-Like Particles (ALPs) and other rare processes in similar fixed-target environments.

In summary, the paper successfully validates the simulation tools used for the SHiP experiment, quantifies the background from $J/\psi$ decays in a realistic thick-target scenario, and places stringent limits on secondary production mechanisms.