Observation of $ψ(3686) \to n\bar{n}$ and improved measurement of $ψ(3686) \to p \bar{p}$

Using a sample of $1.07\times 10^8$ $ψ(3686)$ events collected by the BESIII detector, this study reports the first observation of the decay $ψ(3686) \to n\bar{n}$ and provides improved measurements of the branching fractions and polar angular distribution parameters for both $ψ(3686) \to n\bar{n}$ and $ψ(3686) \to p\bar{p}$ decays.

The Gist

Imagine the subatomic world as a bustling, high-energy dance floor. In the center of this floor sits a very heavy, short-lived celebrity named $\psi(3686)$ (pronounced "psi-three-six-eight-six"). This particle is a "charmonium" state, which is essentially a heavy couple made of a charm quark and an anti-charm quark holding hands.

Because this celebrity is unstable, they eventually break up. Sometimes, they break up into a pair of light, fast-moving dancers: a proton and an antiproton (matter and antimatter twins). Other times, they break up into a neutron and an antineutron (the neutral twins).

For decades, physicists have watched the proton-antiproton breakup, but the neutron-antineutron breakup was a ghost story—no one had ever actually seen it happen. This paper is the moment the ghost finally appeared.

Here is the story of what the BESIII Collaboration (a team of scientists from around the world) discovered, explained simply:

1. The Big Catch: Seeing the Invisible

The scientists used a massive, high-tech camera called the BESIII detector (located in Beijing) to watch 107 million of these $\psi(3686)$ celebrities break up.

• The Proton Discovery (The Improved Measurement): They re-measured the proton breakup. Think of this like taking a blurry photo of a famous actor and then taking a crystal-clear, high-definition portrait. They found the rate at which this happens is about 3 out of every 10,000 breakups. This is a very precise measurement, much better than previous attempts.
• The Neutron Discovery (The First Time): This was the big headline. Neutrons are tricky because they have no electric charge; they don't leave a trail in the detector like protons do. They are like ghosts that only reveal themselves when they crash into the detector's walls and explode into a shower of energy.
  • The team used a clever computer algorithm (a "Boosted Decision Tree," which is like a super-smart detective) to sift through millions of background noises to find the specific pattern of a neutron crashing.
  • Result: They found it! They observed the neutron-antineutron breakup for the first time. It happens at almost the exact same rate as the proton breakup (also about 3 in 10,000).

2. The Dance Move: The "Angle" of the Breakup

When these particles break up, they don't just fly off randomly. They have a specific "dance style." The paper measures a parameter called $\alpha$ (alpha), which describes how the particles fly apart relative to the direction of the collision.

• The Proton Dance: The protons and antiprotons fly out in a very specific, predictable pattern (like a figure-eight or a dumbbell shape). The math says their dance style is very "standard" (close to the theoretical maximum).
• The Neutron Dance: Here is the surprise! The neutrons and antineutrons dance differently. Their pattern is less "dumbbell-like" and more spread out.
  • Why this matters: In the simpler cousin of this particle (called $J/\psi$), protons and neutrons dance almost identically. But in this heavier $\psi(3686)$ version, they dance differently. This suggests that the "music" (the forces of nature) driving the breakup is more complex than we thought. It's like two twins who usually dress the same, but suddenly one wears a tuxedo and the other wears a t-shirt.

3. The "12% Rule" Mystery

In the world of particle physics, there is a famous rule of thumb called the "12% Rule." It predicts that if a heavy particle breaks up into something, the heavier version of that particle should break up into the same thing about 12.7% of the time compared to the lighter version.

• The scientists checked this rule for both protons and neutrons.
• The Verdict: The rule holds up! The ratios they measured were roughly 14.4% and 14.8%. This is close enough to 12.7% to say, "Okay, the rule works here." This is good news because it helps physicists understand how the strong force (the glue holding atoms together) works at different energy levels.

4. Why Should You Care?

You might ask, "Who cares about a particle breaking up into neutrons?"

• It's a Puzzle Piece: The universe is held together by the "Strong Force," but we don't fully understand how it works at low energies. It's like knowing how a car engine runs, but not understanding the specific chemistry of the fuel.
• The "Ghost" Hunt: Finding the neutron breakup confirms that our detectors are good enough to see the "invisible" particles.
• The Anomaly: The fact that protons and neutrons dance differently in this specific decay, but similarly in others, hints that there might be a hidden mechanism or a "long-distance" interaction happening that we haven't fully mapped out yet.

The Bottom Line

This paper is a victory for precision. The team successfully:

1. Found the "Ghost": Observed the $\psi(3686) \to n\bar{n}$ decay for the first time.
2. Sharpened the Lens: Measured the proton decay with much higher accuracy.
3. Spotted a Rhythm Change: Discovered that protons and neutrons behave differently in this specific decay, challenging our current theories and inviting further investigation.

It's a bit like finding a new note in a song you've heard a thousand times, realizing the melody is more complex than you thought, and now you have to rewrite the sheet music for the whole orchestra.

Technical Summary

1. Problem and Motivation

The paper addresses the need to understand the strong interaction in the non-perturbative and transition energy regimes of Quantum Chromodynamics (QCD). Specifically, it focuses on the charmonium resonance $\psi(3686)$ (often denoted as $\psi'$).

• The "12% Rule" Puzzle: Perturbative QCD predicts that the ratio of branching fractions for $\psi(3686)$ decays to hadrons versus $J/\psi$ decays to the same hadrons should be approximately 12.7% (the "12% rule"). While this holds for many inclusive processes, it has been violated in exclusive channels (e.g., the "$\rho\pi$ puzzle"). Precise measurements of baryon-antibaryon ($N\bar{N}$) decays are crucial to test this rule.
• Missing Data: While $\psi(3686) \to p\bar{p}$ had been measured previously, $\psi(3686) \to n\bar{n}$ had never been observed. Measuring both allows for tests of flavor $SU(3)$ symmetry.
• Phase Angle and Angular Distributions: The relative phase between strong and electromagnetic amplitudes in these decays is a subject of theoretical debate. Furthermore, the angular distribution of the final states follows $dN/d\cos\theta \propto 1 + \alpha \cos^2\theta$. Previous measurements of the parameter $\alpha$ for $\psi(3686) \to p\bar{p}$ had large uncertainties, and no data existed for the neutron channel. Understanding $\alpha$ helps probe QCD helicity conservation and hadron mass effects.

2. Methodology

The analysis utilizes a data sample of $1.07 \times 10^8$ $\psi(3686)$ events collected by the BESIII detector at the BEPCII collider. An off-resonance data sample ($\sqrt{s} = 3.65$ GeV) was used to estimate non-resonant backgrounds.

A. Measurement of $\psi(3686) \to n\bar{n}$

• Event Topology: The final state consists of a neutron ($n$) and antineutron ($\bar{n}$) with no charged tracks. They interact in the Electromagnetic Calorimeter (EMC) producing showers.
• Antineutron Identification: The $\bar{n}$ is expected to have a higher interaction probability and larger deposited energy than the $n$ due to annihilation in the detector.
• Multivariate Analysis (MVA): To suppress background efficiently while maintaining high signal efficiency, a Boosted Decision Tree (BDT) was employed.
  • Variables: 14 variables were used, including energies, number of hits, second and lateral moments, and shower counts for the two leading shower groups (SGs) and remaining showers.
  • Training: Signal MC samples and a weighted mix of off-resonance data and inclusive MC backgrounds were used for training.
• Selection: Events were required to have no charged tracks in the Main Drift Chamber (MDC). The BDT selection rejected ~95% of background while retaining 76% of signal.
• Efficiency Correction: Neutron and antineutron detection efficiencies were corrected as a function of $\cos\theta$ using control samples from $\psi(3686) \to p\bar{n}\pi^- + c.c.$ to account for differences between data and MC simulation.

B. Measurement of $\psi(3686) \to p\bar{p}$

• Event Topology: Two back-to-back charged tracks (proton and antiproton) in the MDC.
• Selection Criteria:
  • Vertex constraints ($V_r < 1.0$ cm, $|V_z| < 10.0$ cm).
  • Momentum range: $1.546 < p < 1.628$ GeV/c.
  • Particle Identification (PID): Likelihood ratios for protons/antiprotons vs. kaons ($L_p > 0.001$ and $L_p > L_K$).
  • Opening angle: $\theta_{open} > 3.1$ rad.
• Background Estimation: Continuum background ($e^+e^- \to p\bar{p}$) was estimated using off-resonance data. Non-$p\bar{p}$ $\psi(3686)$ decays were found to be negligible.
• Efficiency Correction: Tracking and PID efficiencies were corrected using control samples of $\psi(3686) \to p\bar{p}$, comparing data and MC yields in specific momentum and angular bins.

C. Parameter Extraction

• Branching Fractions: Calculated using $B = N_{sig} / (N_{\psi(3686)} \times \epsilon)$, where $N_{sig}$ is the fitted signal yield and $\epsilon$ is the corrected efficiency.
• Angular Distribution ($\alpha$): Fits were performed on the $\cos\theta$ distributions of the neutron/antineutron and proton/antiproton using the function $(1 + \alpha \cos^2\theta)\epsilon(\theta)$.
• Systematic Uncertainties: Extensive studies were conducted covering resolution effects, background modeling, efficiency corrections, binning, trigger efficiency, and physics models.

3. Key Contributions

1. First Observation: This is the first experimental observation of the decay $\psi(3686) \to n\bar{n}$.
2. Improved Precision: The measurement of $\psi(3686) \to p\bar{p}$ is significantly more precise than previous results from E835, BESII, CLEO, and BABAR.
3. Angular Distribution Parameters: Determination of the $\alpha$ parameter for both channels, providing new constraints on theoretical models of baryon production in charmonium decays.
4. Test of the 12% Rule: The results provide updated ratios of $\psi(3686)$ to $J/\psi$ branching fractions to test the "12% rule" in the baryon sector.

4. Results

The measured branching fractions and angular distribution parameters are:

Decay Mode	Branching Fraction ($10^{-4}$)	$\alpha$ Parameter
$\psi(3686) \to n\bar{n}$	$3.06 \pm 0.06 \text{ (stat)} \pm 0.14 \text{ (syst)}$	$0.68 \pm 0.12 \text{ (stat)} \pm 0.11 \text{ (syst)}$
$\psi(3686) \to p\bar{p}$	$3.05 \pm 0.02 \text{ (stat)} \pm 0.12 \text{ (syst)}$	$1.03 \pm 0.06 \text{ (stat)} \pm 0.03 \text{ (syst)}$

• Branching Fraction Ratio: The ratio of branching fractions for neutrons and protons is consistent, supporting $SU(3)$ symmetry expectations.
• Comparison to $J/\psi$:
  • $B(\psi(3686) \to p\bar{p}) / B(J/\psi \to p\bar{p}) = 14.4 \pm 0.6\%$
  • $B(\psi(3686) \to n\bar{n}) / B(J/\psi \to n\bar{n}) = 14.8 \pm 1.2\%$
  • Both ratios are consistent with the perturbative QCD "12% rule" prediction ($\approx 12.7\%$).
• Angular Distribution:
  • The $\alpha$ value for $p\bar{p}$ ($1.03$) is close to the QCD helicity conservation prediction of 1, but significantly higher than previous measurements (which favored $\alpha < 1$).
  • The $\alpha$ value for $n\bar{n}$ ($0.68$) is notably different from the $p\bar{p}$ value.

5. Significance

• Theoretical Implications: The discrepancy between the $\alpha$ values for $p\bar{p}$ and $n\bar{n}$ in $\psi(3686)$ decays (unlike in $J/\psi$ decays where they are similar) suggests a more complex decay mechanism for $\psi(3686)$. This may involve significant contributions from long-distance processes or continuum components that differ between the two resonances.
• Phase Angle: The results do not definitively resolve the relative phase angle between strong and electromagnetic amplitudes but provide essential data points. The fact that $\alpha_{p\bar{p}} \approx 1$ while $\alpha_{n\bar{n}} \approx 0.68$ challenges simple models assuming a universal phase angle or identical dynamics for $J/\psi$ and $\psi(3686)$.
• Methodological Benchmark: The successful application of MVA (BDT) for neutral baryon reconstruction sets a precedent for future analyses of similar neutral final states in high-energy physics.

In conclusion, this paper provides the first definitive measurement of $\psi(3686) \to n\bar{n}$ and refines the understanding of $\psi(3686) \to p\bar{p}$, offering critical experimental data to constrain QCD models in the charmonium energy region.