First measurement of $\Sigma^{+}n\rightarrow\Lambda p$ and $\Sigma^{+}n\rightarrow\Sigma^{0}p$ cross sections via $\Sigma^+$-nucleus scattering at an electron-positron collider

Using a large sample of $J/\psi$ events collected by the BESIII detector, this study reports the first observation and measurement of the cross sections for the $\Sigma^{+}n\rightarrow\Lambda p$ and $\Sigma^{+}n\rightarrow\Sigma^{0}p$ reactions via $\Sigma^{+}$-nucleus scattering at an electron-positron collider.

The Gist

The Big Picture: Catching Ghosts in a Machine

Imagine you are trying to study a very shy, fast-moving ghost (a particle called a Sigma-plus baryon). This ghost is so short-lived that it vanishes before you can even look at it directly. Usually, scientists try to study these ghosts by shooting them at a wall and seeing how they bounce off. But making a beam of these ghosts is incredibly hard, expensive, and the ghosts disappear too quickly to travel far.

The BESIII team at the Beijing Electron-Positron Collider (BEPCII) came up with a clever trick: Instead of building a wall, they used the machine itself as the target.

Think of the particle accelerator as a giant, high-speed racetrack. The "track" (the beam pipe) is made of specific materials like gold, beryllium, and carbon. The team created a massive number of these "ghosts" inside the track. As the ghosts zoomed around, some of them crashed into the atoms making up the track itself. By studying the debris from these tiny crashes, the scientists could figure out how the ghosts behave when they hit a neutron (a building block of atoms).

The Main Characters

1. The Sigma-plus ($\Sigma^+$): The "Ghost." It's a type of hyperon (a heavy cousin of the proton/neutron). It lives for a split second before decaying.
2. The Neutron: The "Target." It's hiding inside the atoms of the beam pipe (specifically in Beryllium, Carbon, and Gold).
3. The J/$\psi$ Particle: The "Factory." The machine smashes electrons and positrons together to create this heavy particle, which immediately splits into a pair of ghosts: a $\Sigma^+$ and an anti-ghost ($\bar{\Sigma}^-$).
4. The Neutron Star: The "Mystery." In the deep core of a neutron star, gravity is so strong that neutrons might turn into these "ghosts." But we don't know exactly how they interact, and this mystery is called the "Hyperon Puzzle."

The Experiment: A Game of "Pin the Tail on the Donkey"

The scientists collected data from about 10 billion particle collisions. Here is how they found the specific interactions they were looking for:

1. The Setup: They created a $\Sigma^+$ and an anti-$\Sigma^-$ pair.
2. The Crash: The $\Sigma^+$ zoomed out and hit a neutron inside the beam pipe.
3. The Transformation:
   • Sometimes, the $\Sigma^+$ hit the neutron and turned into a Lambda ($\Lambda$) particle and a proton.
   • Other times, it turned into a Sigma-zero ($\Sigma^0$) and a proton.
4. The Clues: The scientists couldn't see the crash directly. Instead, they looked for the "footprints" left behind.
   • They tracked the proton and the Lambda particle.
   • They looked for a "missing" piece of the puzzle (the neutron from the pipe) by calculating the recoil (the pushback).
   • They used a special mathematical fit (like finding a specific shape in a pile of sand) to separate the real signals from the background noise.

The Results: Measuring the "Bounce"

The team successfully measured the cross-section for these reactions.

• What is a cross-section? Imagine throwing a ball at a target. The "cross-section" is the size of the target area that the ball needs to hit to cause a specific reaction. A larger cross-section means the reaction happens more often; a smaller one means it's rare.

They found:

• The reaction turning into a Lambda happens with a cross-section of about 45 mb (millibarns).
• The reaction turning into a Sigma-zero happens with a cross-section of about 30 mb.

(Note: "mb" is a tiny unit of area, roughly the size of an atomic nucleus.)

Why Does This Matter? (Solving the Neutron Star Puzzle)

This is the most exciting part. Inside a Neutron Star, gravity is crushing everything together. Scientists think that under this pressure, neutrons might turn into hyperons (like our $\Sigma^+$).

However, there is a problem called the "Hyperon Puzzle."

• The Theory: If hyperons appear, they make the star "squishier" (less pressure).
• The Observation: We see neutron stars that are very heavy (twice the mass of our Sun). If they were "squishy," they would collapse into black holes.
• The Conflict: Our current theories say the stars should collapse, but they don't.

By measuring exactly how these particles interact (the "bounce" or cross-section), scientists can refine their theories. They are looking for a "secret handshake" (a three-body force) between the particles that might make the star stiffer and able to hold up that extra weight.

The "Firsts" and the Future

• First Time: This is the first time anyone has ever measured these specific interactions ($\Sigma^+ + n$) at an electron-positron collider. Before this, we had to rely on very old, low-quality data from the 1960s and 70s.
• The Method: They proved that you can use the machine's own beam pipe as a target. It's like using the walls of a bowling alley as the pins.
• The Future: Now that they know this works, they can study even shorter-lived particles in the future. With more data from bigger machines, they hope to map out exactly how these particles behave at different speeds, finally solving the mystery of why neutron stars don't collapse.

Summary Analogy

Imagine you are trying to understand how two specific types of Lego bricks snap together, but you can't buy the bricks.

1. Old Way: You wait for a rare delivery truck to drop a few bricks, then try to snap them together before they fall apart. (Hard, rare, messy).
2. BESIII Way: You build a giant machine that spits out millions of these bricks every second. You line the floor with other Lego bricks (the beam pipe). As the flying bricks hit the floor bricks, they snap together and break apart. You film the explosion and count the pieces.
3. The Result: You now know exactly how strong the snap is. This helps you build a model of a giant Lego tower (a neutron star) that doesn't fall over, solving a mystery that has puzzled builders for decades.

Technical Summary

1. Problem Statement and Motivation

• The Hyperon Puzzle: Understanding the Equation of State (EoS) of neutron stars is a major challenge in nuclear astrophysics. Theoretical models predict that hyperons (baryons containing strange quarks) should appear in the dense cores of neutron stars. However, the inclusion of hyperons typically softens the EoS, predicting maximum neutron star masses lower than those observed (the "hyperon puzzle"). Resolving this requires precise knowledge of hyperon-nucleon (YN) interactions, particularly three-body forces and $\Lambda$-$\Sigma$ coupling.
• Data Scarcity: Experimental data on $\Sigma$-nucleon scattering is extremely limited due to the short lifetimes of hyperons and the difficulty of producing intense, monoenergetic hyperon beams. Previous measurements have been sparse and often inconsistent with modern theoretical models (e.g., chiral effective field theory).
• Specific Gap: There has been no prior measurement of $\Sigma^+$-nucleon scattering at an electron-positron ($e^+e^-$) collider. Furthermore, the specific reactions $\Sigma^+n \to \Lambda p$ (charge exchange) and $\Sigma^+n \to \Sigma^0 p$ (elastic/isospin exchange) had not been observed in this context, despite their importance for understanding charge symmetry breaking and $\Lambda$-$\Sigma$ mixing.

2. Methodology

The study utilizes a novel experimental approach using the BESIII detector at the BEPCII storage ring.

• Data Source: The analysis is based on a sample of $(1.0087 \pm 0.0044) \times 10^{10}$ $J/\psi$ events.
• Hyperon Beam Generation: $\Sigma^+$ hyperons are produced via the decay $J/\psi \to \Sigma^+ \bar{\Sigma}^-$. These $\Sigma^+$ baryons are quasi-monoenergetic with a momentum of $0.992 \pm 0.015$ GeV/c.
• Target Material: Instead of a traditional target, the beam pipe material itself serves as the target. The beam pipe consists of Gold ($^{197}\text{Au}$), Beryllium ($^9\text{Be}$), and oil (containing $^{12}\text{C}$ and Hydrogen). The $\Sigma^+$ baryons interact with neutrons within these nuclei.
• Reaction Channels: The study focuses on two processes:
  1. $\Sigma^+ + n \to \Lambda + p$
  2. $\Sigma^+ + n \to \Sigma^0 + p$ (followed by $\Sigma^0 \to \gamma \Lambda$)
• Event Reconstruction:
  • The final state for the first channel is reconstructed as $p \bar{p} \pi^- \gamma \gamma$ (via $\bar{\Sigma}^- \to \bar{p}\pi^0 \to \bar{p}\gamma\gamma$ and $\Lambda \to p\pi^-$).
  • The final state for the second channel includes an additional photon from the $\Sigma^0$ decay.
  • Vertexing: A crucial selection criterion is the distance ($R_{xy}$) of the reconstructed $\Lambda p$ vertex from the beam pipe axis. A clear excess of events is observed near the beam pipe, distinguishing signal from background.
  • Kinematic Fits: Constraints are applied to invariant masses ($M(\bar{p}\pi^0)$, $M(p\pi^-)$, $M(\gamma\Lambda)$) and recoil masses to suppress backgrounds (e.g., from $J/\psi \to \Sigma^+ \bar{\Sigma}^-$ with $\Sigma^+ \to p\pi^0$).
• Simulation: A Geant4-based Monte Carlo (MC) simulation models the detector geometry, response, and the specific interaction of $\Sigma^+$ with the beam pipe material. The simulation assumes the $\Sigma^+$ interacts with a single neutron on the nuclear surface.

3. Key Contributions

• First Observation: This is the first observation of the reactions $\Sigma^+n \to \Lambda p$ and $\Sigma^+n \to \Sigma^0 p$.
• Novel Experimental Technique: It demonstrates the feasibility of using an electron-positron collider and the beam pipe material as a target to study short-lived hyperon-nucleon scattering, a method previously applied to $\Xi^0$, $\Lambda$, and $\bar{\Lambda}$ by BESIII but now extended to $\Sigma^+$.
• Cross-Section Measurement: The paper provides the first direct measurement of the cross-sections for these specific reactions at a center-of-mass energy corresponding to a $\Sigma^+$ momentum of $\approx 0.992$ GeV/c.

4. Results

The analysis identified clear signals for both reactions after background subtraction and fitting the $R_{xy}$ distribution and the invariant mass $M(\gamma\Lambda)$.

• Signal Yields:
  • Total signal events ($\Sigma^+n \to \Lambda p + \Sigma^+n \to \Sigma^0 p$): $126.2 \pm 13.4$.
  • Separated $\Sigma^+n \to \Sigma^0 p$ events: $48.6 \pm 15.9$.
  • Separated $\Sigma^+n \to \Lambda p$ events: $77.6 \pm 20.8$.
• Measured Cross-Sections (on $^9\text{Be}$):
  • $\sigma(\Sigma^+ + ^9\text{Be} \to \Lambda + p + X) = 45.2 \pm 12.1 (\text{stat}) \pm 7.2 (\text{sys}) \text{ mb}$.
  • $\sigma(\Sigma^+ + ^9\text{Be} \to \Sigma^0 + p + X) = 29.8 \pm 9.7 (\text{stat}) \pm 6.9 (\text{sys}) \text{ mb}$.
• Extracted Single-Neutron Cross-Sections:
  Assuming an effective number of reaction neutrons in $^9\text{Be}$ is approximately 3, the cross-sections for a single neutron interaction are derived:
  • $\sigma(\Sigma^+ n \to \Lambda p) = 15.1 \pm 4.0 (\text{stat}) \pm 2.4 (\text{sys}) \text{ mb}$.
  • $\sigma(\Sigma^+ n \to \Sigma^0 p) = 9.9 \pm 3.2 (\text{stat}) \pm 2.3 (\text{sys}) \text{ mb}$.
• Comparison with Theory: The measured single-neutron cross-sections are in agreement with predictions from leading-order covariant chiral effective field theory (Ref. [28]).

5. Significance

• Resolving the Hyperon Puzzle: These measurements provide critical empirical constraints on the $\Sigma$-nucleon interaction strength. This data is essential for refining the Equation of State (EoS) of neutron stars and understanding whether hyperons can exist in their cores without violating observed mass limits.
• Validating Theoretical Models: The results offer a benchmark for theoretical models (constituent quark models, meson-exchange, and chiral EFT) regarding $\Sigma$-nucleon scattering, particularly the $\Lambda$-$\Sigma$ coupling strength.
• Methodological Advancement: The study proves that $e^+e^-$ colliders can serve as unique facilities for hyperon physics, capable of studying reactions that are endoergic (requiring energy input) or involve very short-lived particles that are difficult to produce in traditional fixed-target experiments.
• Future Prospects: The success of this method paves the way for future studies at super tau-charm facilities with higher statistics, allowing for momentum-dependent cross-section studies and the exploration of other hyperon-nucleon channels.