First measurement of $ϕ$ meson production in 30 GeV proton-nucleus reactions via di-electron decay at J-PARC

This paper reports the first measurement of $\phi$ meson production via the di-electron decay channel in 30 GeV proton-carbon and proton-copper interactions at J-PARC, yielding total cross sections of 2.0 mb and 10.3 mb respectively and establishing a mass-number dependence parameter $\alpha$ of 0.99 that aligns with existing proton-proton data.

The Gist

Imagine the universe is a giant, complex machine, and inside it, tiny particles called protons are zooming around at incredible speeds. Scientists want to understand how these protons behave when they crash into other things, like the nuclei of atoms in a piece of metal.

This paper is like a report card from a very specific, high-tech experiment that just happened at a massive particle accelerator in Japan called J-PARC. Here is the story of what they did, explained simply.

The Goal: Catching a "Ghost" Particle

The scientists were looking for a specific, short-lived particle called the $\phi$ (phi) meson.

• The Analogy: Think of the $\phi$ meson as a ghost that appears for a split second when two particles crash, and then immediately vanishes. Because it vanishes so fast, you can't see it directly.
• The Clue: When the ghost vanishes, it leaves behind a "fingerprint" in the form of two tiny particles: an electron and a positron (a pair of oppositely charged twins). The scientists built a giant camera (the E16 spectrometer) to catch these twins. If they find the twins moving in a specific way, they know the ghost ($\phi$ meson) was there.

The Setup: A High-Speed Train and a Target

1. The Train: They used a beam of protons traveling at 30 GeV (which is like a train moving at 99.9% of the speed of light). This is a brand-new track at the J-PARC facility, like a newly opened high-speed railway line.
2. The Targets: They didn't just crash the train into a wall; they aimed it at two different "targets":
   • A thin sheet of Carbon (light, like a piece of paper).
   • A thin sheet of Copper (heavier, like a thick coin).
3. The Camera: The E16 spectrometer is a massive, complex detector surrounding the target. It's like a high-speed security system with layers of sensors that can tell exactly where the "twin" particles went and how fast they were moving.

The Experiment: The "First Run"

This paper reports on the very first time they successfully caught these $\phi$ mesons using this new machine and this specific energy level. It was a "commissioning run," meaning they were testing the equipment to make sure it worked before doing the big, long-term experiments.

They fired billions of protons at the Carbon and Copper targets. Most of the time, nothing interesting happened. But occasionally, a proton would hit a nucleus, create a $\phi$ meson, and that meson would instantly turn into the electron-positron twins. The camera caught these twins.

The Results: Counting the Ghosts

After sorting through millions of data points, the scientists found:

• On Carbon: They found about 12 of these ghost events.
• On Copper: They found about 24 of these ghost events.

Because Copper is heavier (it has more "stuff" inside the nucleus) than Carbon, they expected to find more ghosts there. And they did!

The Big Question: How does size matter?

The scientists wanted to know a specific rule: If you double the size of the target, do you get double the ghosts?

In physics, they use a number called $\alpha$ (alpha) to describe this relationship.

• If $\alpha = 1$, it means the production is perfectly proportional to the size of the target (like buying more tickets for a bigger theater).
• If $\alpha < 1$, it means the bigger target actually hides or suppresses the ghosts (maybe the ghosts get stuck inside the heavy target).
• If $\alpha > 1$, it means the heavy target boosts the production.

The Finding:
Their calculation gave them an $\alpha$ value of roughly 1.0.

• Translation: This is great news! It means that at this energy level, the $\phi$ mesons are produced in a very straightforward way. The size of the target (Carbon vs. Copper) doesn't change the rules of the game. The "ghosts" are just as likely to appear in a heavy nucleus as they are in a light one, relative to the amount of material.

Why Does This Matter?

1. It's a New Era: This is the first time this has been measured at this specific energy (30 GeV) using this specific method (looking for electron twins). It fills a gap in our knowledge map.
2. It Validates the Machine: The fact that the results match what we expect from other experiments (at different energies) proves that the new J-PARC beamline and the E16 camera are working perfectly.
3. Future Physics: Now that they know the "baseline" rules (how the ghosts behave in normal matter), they can start looking for weird things. In the future, they will smash protons into hot, dense matter (like the stuff inside a neutron star) to see if the rules change. If the rules change there, it could tell us about the fundamental forces that hold the universe together.

In a Nutshell

The scientists built a new, super-fast particle accelerator track and a giant camera. They fired protons at light and heavy metal targets to catch a fleeting particle called the $\phi$ meson. They successfully caught it, counted it, and confirmed that the rules of how these particles are made haven't changed at this energy level. It's a successful "shakedown cruise" for a new scientific instrument, paving the way for deeper discoveries about the universe's building blocks.

Technical Summary

1. Problem and Motivation

The paper addresses the need to understand hadron production mechanisms in the intermediate energy region (around 30 GeV, $\sqrt{s} \approx 7.7$ GeV). In this regime, perturbative QCD (pQCD) is less reliable, and non-perturbative reaction mechanisms dominate.

• Scientific Context: There is significant interest in high-density QCD matter and the restoration of chiral symmetry. Strange hadron production (specifically $\phi$ mesons) is a key probe for these phenomena.
• The Gap: While $\phi$ meson production has been studied at low energies (KEK-PS) and high energies (CERN SPS), there was a lack of data in the 30 GeV region using the di-electron decay channel ($\phi \to e^+e^-$). The di-electron channel is a "penetrating probe" that escapes the nuclear medium without strong interaction, making it ideal for studying in-medium modifications.
• Objective: To perform the first measurement of $\phi$ meson production in proton-nucleus ($p+A$) collisions at 30 GeV to determine the total production cross-section and investigate the dependence on the nuclear mass number ($A$).

2. Methodology

Experimental Setup

• Facility: J-PARC Hadron Experimental Facility, utilizing the newly commissioned High-Momentum Beamline (operational since 2020).
• Beam: 30 GeV proton beam with an intensity of $1 \times 10^{10}$ protons/spill.
• Targets: Three thin foils were used to minimize radiation length and allow vertex separation:
  • Carbon (C): 0.5 mm thick.
  • Copper (Cu): Two foils, 0.08 mm thick each (placed at $z = \pm 20$ mm).
• Spectrometer (E16): Designed for high-rate capability and large acceptance.
  • Tracking: Gas Electron Multiplier trackers (GTR) and Silicon Strip Detectors (STS).
  • Electron Identification (EID):
    • Hadron Blind Detector (HBD): A gas Cherenkov detector using CF$_4$ to reject pions (threshold 4.2 GeV/c).
    • Lead-Glass (LG) Calorimeter: 8 radiation lengths deep to distinguish electrons from pions via $E/p$ ratio.
  • Magnet: A dipole "FM magnet" providing a 1.77 T field.

Data Acquisition and Selection

• Data: Collected during a commissioning run in 2024 ($2.28 \times 10^4$ spills).
• Trigger: Required a triple coincidence of GTR, HBD, and LG hits with at least two electron candidates. A wide opening angle ($>45^\circ$) was required to suppress photon conversions.
• Reconstruction:
  • Tracks reconstructed using Runge-Kutta fitting.
  • Vertex selection ensured tracks originated from the same target foil.
  • Invariant mass calculated from $e^+e^-$ pairs.

Analysis and Corrections

• Efficiency: Evaluated using embedding methods (embedding low-intensity calibration waveforms into real data) and calibration runs. Total reconstruction efficiency was ~31%.
• Normalization: Beam intensity was monitored via an ion chamber, corrected for trigger vetoes and DAQ live time to determine the number of "recorded protons" ($1.21 \times 10^{14}$).
• Cross-Section Calculation: Measured yields were converted to total cross-sections ($\sigma$) using the kinematic distributions from the JAM event generator (v1.011) to model detector acceptance.
• Mass Dependence: The production mechanism was characterized by the parameter $\alpha$ in the relation $\sigma \propto A^\alpha$.

3. Key Contributions

• First Measurement: This is the first physics result from the J-PARC E16 experiment and the first measurement of $\phi$ meson production in $p+A$ reactions at 30 GeV via the di-electron channel.
• Validation of Beamline: Successfully demonstrated the capability of the new J-PARC high-momentum beamline to deliver stable, high-intensity beams for precision physics.
• Methodological Benchmark: Established a robust framework for measuring rare di-electron signals in high-multiplicity environments using the E16 spectrometer, including detailed efficiency evaluations and systematic uncertainty quantification.

4. Results

Production Yields and Cross-Sections

The $\phi$ meson signal was successfully reconstructed in both Carbon and Copper targets.

• Carbon Target:
  • Yield: $11.9 \pm 5.6 \text{ (stat)} \pm 5.2 \text{ (syst)}$
  • Total Cross Section: $2.0 \pm 0.9 \text{ (stat)} \pm 1.0 \text{ (syst)}$ mb
• Copper Target:
  • Yield: $23.6 \pm 10.2 \text{ (stat)} \pm 8.5 \text{ (syst)}$
  • Total Cross Section: $10.3 \pm 4.4 \text{ (stat)} \pm 4.4 \text{ (syst)}$ mb

Mass Number Dependence ($\alpha$)

The parameter $\alpha$ was extracted to describe the scaling of the cross-section with the nuclear mass number ($A$).

• Calculated $\alpha$: $0.99 \pm 0.38 \text{ (stat)} \pm 0.34 \text{ (syst)}$
• Interpretation: An $\alpha \approx 1$ implies that the production cross-section scales linearly with the mass number ($\sigma \propto A$). This suggests that $\phi$ meson production is not suppressed by nuclear matter effects (which would imply $\alpha < 1$, e.g., surface production) nor enhanced (which would imply $\alpha > 1$).

Comparison with Other Data

• The extrapolated cross-section for proton-proton ($A=1$) collisions at 30 GeV agrees well with existing measurements at comparable energies (e.g., NA61/SHINE data at 40 GeV/c).
• The derived $\alpha$ value is consistent with previous measurements at 12 GeV (KEK-PS) and 400 GeV (CERN SPS), indicating that the production mechanism remains proportional to the nuclear mass number across this wide energy range.

5. Significance

• Baseline for In-Medium Studies: The measurement of $\phi$ production in normal nuclear density (proton-nucleus) provides a crucial baseline for the primary goal of the E16 experiment: studying in-medium spectral modifications of the $\phi$ meson in heavy-ion collisions. Without this baseline, distinguishing between vacuum production and medium effects is impossible.
• QCD Matter Constraints: The result ($\alpha \approx 1$) supports the hypothesis that $\phi$ production in this energy regime is not significantly suppressed by nuclear absorption, constraining theoretical models of hadron-nucleus interactions.
• Future Outlook: This successful pilot measurement validates the experimental setup for future high-statistics runs, which will aim to observe potential signals of chiral symmetry restoration and degeneracy of chiral partners in the dilepton spectrum.