Comprehensive measurement of $η^\prime$ photoproduction off the proton at $E_γ< 2.4$ $\mathrm{GeV}$

This paper presents a comprehensive measurement of photon beam asymmetries, total, and differential cross sections for $\eta'$ photoproduction off the proton up to 2.32 GeV, providing new constraints for amplitude decomposition and suggesting a potentially larger coupling of the $\eta'$-nucleon system to the $N(2250)$ resonance.

The Gist

Imagine the nucleus of an atom as a tiny, bustling city. Inside this city live the protons and neutrons (collectively called nucleons). For a long time, scientists thought these nucleons were like simple Lego bricks made of just three smaller pieces (quarks). But recently, physicists have realized that the "city" is much more complex than that. There are hidden structures, strange vibrations, and temporary "ghost" particles popping in and out that our current Lego models can't explain.

To solve this mystery, scientists need to take a closer look at how these nucleons vibrate and change when hit with energy. This is called baryon spectroscopy.

Here is a breakdown of what this paper did, using simple analogies:

1. The Experiment: A High-Speed Pinball Machine

The researchers used a giant machine at a facility in Japan called SPring-8. Think of this as a high-tech pinball machine.

• The Ball: Instead of a metal ball, they shot a beam of photons (particles of light) at a target made of liquid hydrogen (which is just protons).
• The Goal: They wanted to see what happens when a photon hits a proton. Specifically, they were looking for a rare event where the proton gets excited and spits out a very heavy, strange particle called an $\eta'$ (eta-prime) meson.
• The Catch: The $\eta'$ is like a "heavy ghost." It's very heavy for its size and decays (falls apart) almost instantly into other particles. Because it's so heavy, it requires a lot of energy to create, and because it disappears so fast, it's very hard to catch.

2. The Detective Work: Two Ways to Catch the Ghost

Since the $\eta'$ vanishes immediately, the scientists couldn't see it directly. Instead, they had to look at the "footprints" it left behind. The $\eta'$ usually leaves footprints in two different ways:

1. The Two-Photon Trail: It splits into two light particles ($\gamma\gamma$).
2. The Six-Photon Trail: It splits into a more complex chain that eventually becomes six light particles ($\pi^0\pi^0\eta \rightarrow 6\gamma$).

The team used a giant, egg-shaped detector (named BGOegg) that surrounds the target like a camera lens. It's so sensitive it can catch these tiny flashes of light. By analyzing both trails simultaneously, they doubled their chances of finding the signal, much like a detective checking two different security cameras to catch a thief.

3. The New Clues: Shining a Light from Different Angles

In previous experiments, scientists mostly measured how many particles were produced (the cross-section). It's like counting how many people walk through a door.

• The New Twist: This team also measured polarization. Imagine shining a flashlight at a wall. If you rotate the flashlight, the shadow changes shape. By rotating the "polarization" of their light beam, the scientists could see how the reaction changed depending on the angle.
• Why it matters: This is the "smoking gun." Just counting people (cross-section) tells you how busy the door is, but watching the shadows (polarization) tells you who is walking through and how they are moving. This helps distinguish between different types of hidden resonances (excited states of the proton).

4. The Discovery: A New "Resonance" Candidate?

When the scientists analyzed their new, high-precision data, they compared it to existing computer models (like a "Wanted Poster" for known particles).

• The Surprise: The data didn't quite fit the old models perfectly.
• The Implication: The results suggest that there might be a specific, heavy, high-spin resonance called N(2250) that interacts much more strongly with the $\eta'$ meson than we thought.
• The Analogy: Imagine you are trying to identify a singer by listening to their voice. You have a list of known singers. The new data sounds like a mix of known singers, but there's a specific high note that only one obscure singer (N(2250)) can hit. The new data suggests this obscure singer is actually in the band, and they are louder than we realized.

5. Why This Matters

This paper is a significant step forward because:

• It fills a gap: They measured energies and angles that no one had measured with this level of precision before.
• It challenges the models: The fact that the data hints at a stronger connection to the N(2250) resonance suggests our current understanding of how quarks stick together inside a proton might need an update.
• It's a foundation: This isn't the final answer, but it provides the "new constraints" (tighter rules) that future theories must follow.

In summary: The BGOegg collaboration acted like high-tech detectives, using a powerful light beam and a giant egg-shaped camera to catch a fleeting, heavy particle. By watching how this particle behaves from different angles, they found a clue that suggests a mysterious, heavy "vibration" inside the proton (the N(2250)) is more important to our understanding of the universe than we previously thought.

Technical Summary

1. Problem Statement and Motivation

• Scientific Context: Baryon spectroscopy is crucial for understanding non-perturbative QCD and quark confinement. However, existing baryon spectra in the mass range around 2 GeV are not well explained by constituent quark models or lattice QCD calculations, suggesting complex hadron structures beyond three uncorrelated quarks.
• Specific Gap: The reaction $\gamma p \to \eta' p$ is a valuable probe for high-mass nucleon resonances ($N^*$) in the $s$-channel because the $\eta'$ meson (due to the $U_A(1)$ anomaly) has a large mass and zero isospin, meaning only nucleon resonances contribute.
• Data Deficiencies: Prior experimental data on $\eta'$ photoproduction were scarce and inconsistent:
  • Differential cross-sections ($d\sigma/d\Omega$) from CLAS and CBELSA/TAPS showed systematic magnitude differences.
  • Polarization observables, specifically photon beam asymmetries ($\Sigma$), were limited to energies near the production threshold ($W < 2.08$ GeV).
  • The lack of polarization data hindered the ability to distinguish between amplitude models that cross-sections alone could not differentiate.

2. Methodology and Experimental Setup

• Facility: The experiment was conducted at the SPring-8 LEPS2 beamline (Japan) using the BGOegg detector.
• Beam: A tagged photon beam with high linear polarization was generated via laser Compton scattering.
  • Energy Range: $1.26$–$2.39$ GeV ($W$ up to $2.316$ GeV).
  • Polarization: Up to 92% at the highest energy, dropping to 51% near the threshold.
• Target: A 54 mm-thick liquid hydrogen target.
• Detection System:
  • BGOegg Calorimeter: An egg-shaped array of 1320 Bismuth Germanate (BGO) crystals covering polar angles of $24^\circ$–$144^\circ$. It provided excellent mass resolution for neutral particles.
  • Inner Plastic Scintillators (IPS): Used for charged particle identification and timing.
  • Drift Chamber (DC): A planar hexagonal chamber covering forward angles ($<22^\circ$) for charged particle tracking.
• Reaction Channels: The analysis focused on two $\eta'$ decay modes to maximize statistics:
  1. $\eta' \to \gamma\gamma$ (2$\gamma$ mode)
  2. $\eta' \to \pi^0\pi^0\eta \to 6\gamma$ (6$\gamma$ mode)
• Analysis Techniques:
  • Kinematic Fits: Events underwent 4-constraint (2$\gamma$) or 7-constraint (6$\gamma$) kinematic fits enforcing four-momentum conservation.
  • Background Subtraction: Signal extraction involved fitting invariant mass distributions ($M_{\gamma\gamma}$ and $M_{\pi^0\pi^0\eta}$) using Monte Carlo (Geant4) simulated templates for signal and background (e.g., non-resonant $\pi^0\pi^0p$).
  • Polarization Measurement: Beam asymmetries ($\Sigma$) were extracted by comparing event rates when the reaction plane was parallel vs. perpendicular to the photon polarization vector. Data were collected with both vertical and horizontal polarization to cancel azimuthal detector biases.

3. Key Contributions

• First High-Energy Asymmetry Data: Provided the first measurement of photon beam asymmetries ($\Sigma$) for $\eta'$ photoproduction in the unexplored energy region up to $W = 2.316$ GeV ($E_\gamma = 2.389$ GeV).
• Unprecedented Precision at Backward Angles: Obtained the most precise differential cross-section data to date, specifically at extremely backward $\eta'$ angles ($\cos \theta_{c.m.} \approx -0.9$).
• Combined Decay Mode Analysis: Doubled the signal statistics by simultaneously analyzing both the 2$\gamma$ and 6$\gamma$ decay channels, allowing for robust cross-checks and improved statistical power.
• Comprehensive Dataset: Delivered a complete set of observables ($d\sigma/d\Omega$, $\sigma_{tot}$, and $\Sigma$) over a wide kinematic range, resolving previous systematic discrepancies between CLAS and CBELSA/TAPS data.

4. Results

• Differential Cross Sections ($d\sigma/d\Omega$):
  • Measured in 7 energy bins and 10 polar angle bins.
  • Showed a clear forward enhancement at higher energies (characteristic of $t$-channel exchange).
  • Backward Enhancement: A distinct energy enhancement was observed at the most backward bin ($\cos \theta_{c.m.} = -0.9$) at higher energies, a feature also seen in $\eta$ photoproduction, potentially indicating high-spin resonances or interference effects.
  • The results were statistically consistent with CLAS data in overlapping regions but showed systematic deviations from CBELSA/TAPS values.
• Total Cross Section ($\sigma_{tot}$):
  • Integrated from $d\sigma/d\Omega$.
  • Showed a maximum around $W \approx 2040$ MeV, followed by a gradual decrease.
  • Confirmed the systematic offset with previous CBELSA/TAPS data.
• Photon Beam Asymmetry ($\Sigma$):
  • Values were small at lower energies.
  • Became negative in the mid-angle range around $W \approx 2.1$ GeV, consistent with CLAS observations (suggesting contributions from resonances like $N(1895)$, $N(1900)$, etc.).
  • At higher energies, $\Sigma$ became positive at most angles but showed significant angular dependence, with higher values in the backward bin.
• Partial Wave Analysis (PWA):
  • The new data were fitted using EtaMAID2018 and BG2019 models.
  • Key Finding: The inclusion of the new high-precision $\Sigma$ data significantly improved the fits (reduced $\chi^2$).
  • N(2250) Resonance: The fits implied a significantly larger coupling constant for the $N(2250)$ resonance ($J^P = 9/2^-$) to the $\eta'N$ system. In the EtaMAID2018 fit, the coupling constant increased from 0.085 to 0.598. The BG2019 model, when modified to include $N(2250)$, improved the $\chi^2$ for $\Sigma$ data from 1.8 to 0.9.

5. Significance

• Constraints on Amplitude Decomposition: The new polarization data provide essential constraints that cannot be derived from cross-sections alone, helping to resolve ambiguities in the decomposition of complex amplitudes.
• Evidence for High-Spin Resonances: The results strongly suggest the importance of the high-spin $N(2250)$ resonance in $\eta'$ photoproduction, a feature that was previously unconstrained.
• Future Directions: The study highlights the need for even higher-statistics data to confirm the $N(2250)$ contribution and further explore the "missing" or poorly understood baryon states in the 2 GeV mass region. The paper notes that future analyses using unanalyzed data and larger solid-angle detectors will further refine these measurements.

In summary, this work represents a major advancement in baryon spectroscopy by providing the first comprehensive set of polarization and cross-section data for $\eta'$ photoproduction at high energies, directly challenging existing models and pointing toward the significant role of the $N(2250)$ resonance.