Cross Section Measurements of $\bar{n}p \rightarrow K^{+}K^{-}\pi^{+}(\pi^{0})$ via Antineutrons Produced by $J/\psi \to p \pi^{-} \bar{n}$ Decays

Using a novel method to tag antineutrons from $J/\psi \to p \pi^{-} \bar{n}$ decays within a sample of over 10 million $J/\psi$ events collected by the BESIII detector, researchers measured the cross sections for the inelastic scattering processes $\bar{n}p \rightarrow K^{+}K^{-}\pi^{+}$ and $\bar{n}p \rightarrow K^{+}K^{-}\pi^{+}\pi^{0}$ to be $0.53^{+0.15}_{-0.12} \pm 0.08$ mb and $1.09^{+0.36}_{-0.30} \pm 0.31$ mb respectively, demonstrating the viability of this approach for future studies of antineutron-proton interactions.

The Gist

The Big Picture: Catching Ghosts to Study Collisions

Imagine you want to study how two cars crash into each other, but one of the cars is a "ghost" that you can't see, touch, or steer. You can't just drive the ghost car into a wall and watch what happens.

This is exactly the problem physicists face with antineutrons. They are the "ghost" particles of the universe. They are the antimatter twins of neutrons, but they are incredibly hard to make, hard to control, and they vanish the moment they touch normal matter. Because of this, we know very little about how they interact with protons (the building blocks of atoms).

This paper is about the BESIII Collaboration (a team of scientists at a giant particle collider in China) successfully catching these "ghosts" and crashing them into a target to see what happens.

The Setup: The "Magic Trick" of Creation

Usually, to get a beam of antineutrons, scientists try to smash antiprotons into other particles and hope an antineutron pops out. It's like trying to find a specific needle in a haystack by burning the whole haystack down. It's messy and inefficient.

Instead, this team used a clever "magic trick" involving a particle called the $J/\psi$.

• The Analogy: Imagine the $J/\psi$ is a magician. When the magician performs a trick, they don't just disappear; they split into three things: a proton, a negative pion, and an antineutron.
• The Tag: The proton and the pion are easy to see. The scientists catch them first. Because they know exactly how the magician (the $J/\psi$) works, seeing the proton and pion tells them, "Aha! An antineutron was just created right there!"
• The Result: They don't need a giant machine to shoot antineutrons at a target. They just create them on the fly, right inside their detector, and use the "tag" (the proton/pion pair) to know exactly when and where the ghost antineutron appeared.

The Experiment: The "Oil Layer" Target

Once they "tagged" the antineutron, they needed something for it to crash into.

• The Target: They didn't use a solid block of metal. Instead, they used the oil inside the machine's beam pipe (the tube the particles travel through). This oil contains hydrogen atoms.
• The Collision: The antineutron flies through the oil and smashes into a hydrogen proton.
• The Explosion: When they collide, they don't just bounce off; they shatter and create new particles. In this specific study, the scientists were looking for collisions that produced Kaons (a type of heavy, unstable particle) and Pions (lighter particles).

Think of it like throwing a ghost ball into a bucket of water. When it hits a water molecule, it explodes into a specific spray of bubbles (Kaons and Pions). By counting the bubbles, they can figure out how hard the ghost ball hit.

The Results: Measuring the "Crash"

The team analyzed over 10 billion of these $J/\psi$ events. From that massive pile of data, they found about 15 to 20 perfect examples where an antineutron hit a proton and created the specific spray of particles they were looking for.

They calculated the cross-section, which is a fancy physics way of saying "how big the target looks to the antineutron" or "how likely this crash is to happen."

• Result 1: The crash producing just Kaons and one Pion happens about 0.53 mb (millibarns) of the time.
• Result 2: The crash producing Kaons, a Pion, and a neutral Pion happens about 1.09 mb of the time.

(Note: A "millibarn" is a tiny unit of area, roughly the size of a nucleus. It's like measuring the probability of hitting a specific grain of sand on a beach.)

Why This Matters

1. No "Static" Interference: Unlike antiprotons (which have a negative charge), antineutrons are neutral. This means they don't get pushed away by the electric charge of protons before they even touch. This allows scientists to study the "strong force" (the glue holding atoms together) in its purest form.
2. New Territory: Previous experiments could only study antineutrons moving at low speeds. This new method allows them to study antineutrons moving much faster (up to 1174 MeV/c), opening up a new speed range for exploration.
3. Future Potential: While this study had limited data (only a few dozen events), it proves the method works. It's like finding a new key that unlocks a door we didn't know existed.

The Conclusion

The paper concludes that while they didn't have enough data to study the details of the crash (like what specific intermediate particles were formed in the split second of impact), they successfully proved that this new way of making antineutrons works.

The Takeaway:
Scientists have found a new, efficient way to create "ghost" antineutrons using a particle magician ($J/\psi$). They successfully crashed these ghosts into oil-protons and measured the results. This paves the way for future experiments with even more data, which could help us understand the fundamental forces that hold the universe together.

In short: They caught the ghost, hit the target, and measured the splash.

Technical Summary

1. Problem Statement

Antineutron-proton ($\bar{n}p$) scattering is a crucial process for understanding nucleon-antinucleon interactions. Unlike antiproton-proton ($\bar{p}p$) scattering, $\bar{n}p$ scattering involves only the isospin $I=1$ state and is free from significant Coulomb interactions, making it an ideal laboratory for studying strong interactions. However, experimental data on $\bar{n}p$ scattering is scarce due to the difficulty in producing and controlling antineutron beams. Traditional methods rely on charge-exchange reactions ($\bar{p}p \to \bar{n}n$), which yield low-intensity beams with limited momentum ranges. There is a significant need for new methods to produce antineutrons with higher statistics and broader momentum coverage to investigate inelastic scattering channels, particularly those involving strangeness production (kaons).

2. Methodology

The study utilizes a novel approach to generate antineutrons and measure their scattering cross-sections using the BESIII detector at the BEPCII storage ring.

• Antineutron Source: Antineutrons are produced via the decay $J/\psi \to p\pi^-\bar{n}$. The BESIII experiment collected a dataset of $(10087 \pm 44) \times 10^6$ $J/\psi$ events.
• Tagging Mechanism: The antineutron is "tagged" by detecting the recoil proton ($p$) and pion ($\pi^-$) from the $J/\psi$ decay. A kinematic fit constrains the recoil mass to the nominal antineutron mass, allowing for the determination of the antineutron's momentum (ranging from 0 to 1174 MeV/c) and the tagging efficiency.
• Target: The target protons are provided by the hydrogen ($^1$H) contained in the cooling oil layer of the beam pipe (specifically an oil layer sandwiched between beryllium layers). This eliminates the need for a dedicated external target.
• Signal Reconstruction: The analysis focuses on two inelastic scattering channels:
  1. $\bar{n}p \to K^+K^-\pi^+$
  2. $\bar{n}p \to K^+K^-\pi^+\pi^0$
     Events are selected by reconstructing charged tracks ($K^+, K^-, \pi^+$) and photon candidates (for $\pi^0 \to \gamma\gamma$).
• Background Suppression:
  • Vertexing: A vertex fit is performed on the $K^+K^-\pi^+$ combination. The reconstructed scattering vertex must match the expected hit position on the beam pipe to ensure the interaction occurred in the oil layer.
  • Target Identification: To distinguish scattering off free protons ($^1$H) from scattering off nuclei (e.g., $^9$Be, $^{12}$C), the momentum of the target proton, $P(p)$, is calculated. Events with $P(p) < 0.04$ GeV/c are selected, as free protons in the oil have negligible momentum, whereas nucleons in nuclei have significant Fermi momentum.
  • Kinematic Fit: An unbinned maximum likelihood fit is performed on the energy imbalance variable $\Delta E = E(K^+K^-\pi^+(\pi^0)) - E_{\bar{n}} - m_p$ to extract the signal yield.

3. Key Contributions

• Novel Production Method: Demonstrates the feasibility of using $J/\psi$ decays as a high-yield source of tagged antineutrons, extending the accessible momentum range beyond previous experiments (up to ~1.2 GeV/c).
• First Measurements of Specific Channels: Provides the first measurements of the total cross-sections for $\bar{n}p$ inelastic scattering into final states containing kaons ($K^+K^-\pi^+$ and $K^+K^-\pi^+\pi^0$).
• Validation of Beam-Pipe Targeting: Successfully isolates scattering events from the hydrogen in the beam pipe oil, proving the viability of using passive detector materials as targets for antineutron physics.
• Systematic Uncertainty Evaluation: A comprehensive evaluation of systematic uncertainties, including tracking, particle identification (PID), $\pi^0$ reconstruction, and background from nuclear scattering.

4. Results

The study measured the total cross-sections for the two channels. The results are presented with statistical and systematic uncertainties:

• $\bar{n}p \to K^+K^-\pi^+$:
  • Cross Section: $0.53^{+0.15}_{-0.12} \pm 0.08$ mb
  • (First uncertainty is statistical, second is systematic).
• $\bar{n}p \to K^+K^-\pi^+\pi^0$:
  • Cross Section: $1.09^{+0.36}_{-0.30} \pm 0.31$ mb

Intermediate States:
The invariant mass distributions of the $K^+K^-$ pairs show enhancements around 1.0 GeV/$c^2$ (suggestive of the $\phi$ meson) and 1.5 GeV/$c^2$ (suggestive of the $f_0(1500)$). However, due to limited statistics, the contributions of these intermediate states could not be quantitatively extracted.

Comparison:
The measured cross-section for $\bar{n}p \to K^+K^-\pi^+$ is compared to the isospin-symmetric process $p\bar{p} \to K^+K^-\pi^0$ (measured at 900 MeV/c as 0.347 mb). While a direct comparison is limited by the different momentum ranges and statistics, the results provide a useful benchmark.

5. Significance

• Filling Data Gaps: This work addresses the scarcity of $\bar{n}p$ scattering data, particularly in the strangeness production sector, which is vital for testing theoretical models of nucleon-antinucleon interactions.
• Future Prospects: The observation of "clean" antineutron scattering events validates the method for future high-precision studies. The authors suggest that proposed future $e^+e^-$ colliders in the tau-charm energy region (such as STCF and SCTF) could significantly increase the antineutron flux, enabling differential cross-section measurements and detailed spectroscopy of intermediate states (e.g., glueball candidates like $f_0(1500)$).
• Methodological Advancement: The technique of using $J/\psi$ decays to tag antineutrons and utilizing beam-pipe materials as targets offers a cost-effective and high-statistics pathway for antineutron physics, potentially revolutionizing how such experiments are conducted.