Study of the reactions $\bar{n} p \to 2\pi^{+}\pi^{-}$, $2\pi^{+}\pi^{-}\pi^{0}$, and $2\pi^{+}\pi^{-}2\pi^{0}$ using $J/\psi \to p \pi^{-}\bar{n}$

Using a dataset of $(10.087 \pm 0.044) \times 10^{9}$ $J/\psi$ events collected by the BESIII detector, this study pioneers the investigation of antineutron-proton interactions at an $e^{+}e^{-}$ collider by measuring the cross-sections for the reactions $\bar{n} p \to 2\pi^{+}\pi^{-}$, $2\pi^{+}\pi^{-}\pi^{0}$, and $2\pi^{+}\pi^{-}2\pi^{0}$ across a momentum range extending up to 1174 MeV/$c$.

The Gist

Imagine you are trying to study how two specific types of tiny, invisible billiard balls crash into each other. One ball is a neutron (which has no electric charge), and the other is an antineutron (its "evil twin" with opposite properties).

Usually, scientists study these crashes by firing beams of antineutrons at a target. But making a beam of antineutrons is incredibly hard. It's like trying to catch a ghost with a net; they are rare, hard to control, and they vanish (annihilate) the moment they touch normal matter. Because of this, we have very little data on what happens when these collisions occur at high speeds.

The "Magic Trick" of the Experiment
The scientists in this paper, working with the BESIII detector in China, came up with a clever workaround. Instead of building a giant machine to shoot antineutrons, they used a natural "factory" that already exists in their lab: the J/ψ particle.

Think of the J/ψ particle as a unstable, energetic firework. When it explodes, it sometimes splits into three pieces: a proton, a negative pion (a type of particle), and an antineutron.

• The Setup: The scientists catch the proton and the pion. Because they know exactly how the firework exploded, they can calculate exactly how fast and in which direction the antineutron flew, even without seeing it directly.
• The Target: The antineutron flies out and hits the cooling oil inside the machine's pipe. This oil contains hydrogen atoms. The nucleus of a hydrogen atom is just a single proton. So, the antineutron smashes into a proton sitting almost perfectly still.

What Happened When They Collided?
The team watched what happened when these antineutrons hit the protons. They were looking for specific "debris" left over from the crash. They focused on three types of crashes where the antineutron and proton turned into:

1. Two positive pions and two negative pions.
2. The above, plus one neutral pion (which instantly turns into light).
3. The above, plus two neutral pions.

They did this for antineutrons moving at different speeds, ranging from slow (200 MeV/c) to very fast (up to 1174 MeV/c).

Why This is a Big Deal
Before this experiment, we had almost no data on what happens when antineutrons hit protons at speeds faster than 800 MeV/c. It was a "blind spot" in our understanding of the universe.

• The "Speed Zone": The paper explains that at these higher speeds, the rules of the game change. The particles stop acting like simple marbles and start behaving more like a soup of quarks and gluons (the tiny building blocks inside protons). This experiment is the first time anyone has measured these collisions in that specific "speed zone."
• The Results: They found that at these higher speeds, the crashes produced more complex debris (like the version with two neutral pions) than scientists expected based on slower-speed experiments. It's like discovering that if you throw two cars together at highway speeds, they explode into more pieces than if you just bumped them together in a parking lot.

The "Ghost" in the Machine
The paper also notes something interesting about the debris. They saw clear signs of short-lived "middle-man" particles called rho (ρ) and omega (ω) mesons. Think of these as the shockwaves or the temporary sparks that fly out before the final debris settles. Their presence tells us that these specific "middle-man" particles play a major role in how the antineutron and proton destroy each other.

The Bottom Line
This paper is a "firsts" paper. It is the first time anyone has successfully used an electron-positron collider (a machine designed to smash electrons and positrons) to study how antineutrons interact with protons. They proved that you can use the "debris" from a J/ψ explosion to create a steady stream of antineutrons and study their collisions with protons in the cooling oil.

They filled a huge gap in our knowledge, providing the first map of what happens when antineutrons hit protons at high speeds, a region that was previously completely unexplored. This gives physicists new data to build better theories about how matter and antimatter interact.

Technical Summary

Technical Summary: Study of the Reactions $\bar{n}p \to 2\pi^+\pi^-$, $2\pi^+\pi^-\pi^0$, and $2\pi^+\pi^-2\pi^0$ using $J/\psi \to p\pi^-\bar{n}$

Problem and Motivation
Scattering experiments are fundamental for probing nucleon internal structure, yet the utilization of antineutrons ($\bar{n}$) has been historically limited by production and control challenges. While previous facilities like BNL E-767 and CERN OBELIX successfully generated antineutron beams via the charge-exchange process $\bar{p}p \to \bar{n}n$, these methods suffer from low production rates and difficulties in controlling momentum and direction. Crucially, experimental data for $\bar{n}p$ annihilation cross sections have been non-existent for antineutron momenta exceeding 800 MeV/c. This energy region represents a critical transition in Quantum Chromodynamics (QCD) where degrees of freedom shift from mesons and nucleons to quarks and gluons. The lack of data in this high-momentum regime, extending up to 1174 MeV/c, constitutes a significant gap in understanding nucleon-antinucleon interactions.

Methodology
This study utilizes a novel source of antineutrons produced in the decay $J/\psi \to p\pi^-\bar{n}$, leveraging a dataset of $(10.087 \pm 0.044) \times 10^9$ $J/\psi$ events collected by the BESIII detector at the BEPCII storage ring. The analysis employs a "single-tag" (ST) and "double-tag" (DT) approach:

1. Antineutron Production and Identification: The $\bar{n}$ is identified by reconstructing the $p\pi^-$ pair from the $J/\psi$ decay. The momentum of the $\bar{n}$ is kinematically determined. A Partial Wave Analysis (PWA) of the $J/\psi \to p\pi^-\bar{n}$ decay, utilizing a high-purity sample of $10^5$ events, is used to model the $\bar{n}$ momentum and angular distributions for efficiency corrections.
2. Target Interaction: The target protons are sourced from the hydrogen nuclei ($^1$H) within the cooling oil of the beam pipe. This method isolates interactions with static protons, distinguishing them from background interactions with moving nucleons in gold, beryllium, or carbon nuclei (which exhibit Fermi motion).
3. Event Selection:
   • ST Selection: Reconstructs $p\pi^-$ combinations with kinematic fits constraining the missing mass to the $\bar{n}$ mass.
   • DT Selection: Reconstructs the final state particles from the $\bar{n}p$ interaction: $2\pi^+\pi^-i\pi^0$ (where $i=0, 1, 2$).
   • Background Suppression: A key variable, $P(p_{oil})$, representing the reconstructed momentum of the target proton, is used to reject background events where the proton originates from nuclei with Fermi motion. Signal events are required to have $P(p_{oil}) < 0.035$–$0.045$ GeV/c depending on the channel.
   • Kinematic Constraints: Vertex fits and kinematic fits (1C for $\pi^0$, 4C for ST) are applied to improve resolution. The signal yield is extracted by fitting the $\Delta E$ distribution (the difference between the energy of the final state and the sum of the $\bar{n}$ and static proton energies).

Key Contributions and Results
The paper reports the first measurements of the inelastic scattering cross sections for $\bar{n}p \to 2\pi^+\pi^-$, $\bar{n}p \to 2\pi^+\pi^-\pi^0$, and $\bar{n}p \to 2\pi^+\pi^-2\pi^0$ in the antineutron momentum range of 200 to 1174 MeV/c.

• Cross Sections: The cross sections ($\sigma_i$) are measured in five momentum intervals. The results provide the first experimental data for momenta exceeding 800 MeV/c.
• Channel Comparison: While the $i=1$ channel ($2\pi^+\pi^-\pi^0$) dominates in antiproton-proton annihilation at rest and in lower-momentum OBELIX data, the measurements at higher momenta reveal that the cross section for the $i=2$ channel ($2\pi^+\pi^-2\pi^0$) becomes comparable to, or exceeds, that of the $i=1$ channel across most of the measured range.
• Intermediate States: Invariant mass distributions of the final state pions show clear signals from $\rho$ and $\omega$ intermediate states, indicating significant contributions from these vector mesons in the annihilation process.
• Systematic Uncertainties: Comprehensive systematic uncertainties are evaluated, including contributions from tracking, particle identification, kinematic fit cuts, angular distributions, and efficiency reweighting. The total systematic uncertainties range from approximately 7.5% to 8.4% across the different channels.

Significance
This work represents the first measurement of antineutron-nucleon inelastic scattering at an electron-positron collider. By utilizing the $J/\psi \to p\pi^-\bar{n}$ decay, the study overcomes traditional production challenges, providing a continuous antineutron spectrum and enabling a cross-section scan over a wide momentum range. The results fill a long-standing experimental vacuum for $\bar{n}p$ interactions above 800 MeV/c, offering essential benchmarks for the development of future nucleon-antinucleon ($N\bar{N}$) interaction models. The study demonstrates the feasibility of using $e^+e^-$ colliders to study $\bar{n}$-nucleon interactions, suggesting that future facilities with abundant $J/\psi$ samples, such as the proposed super tau-charm factory, could serve as excellent sources for high-precision studies in nuclear and particle physics.