First observation of the $η_{c}\toΞ^{0} \barΞ^{0}$ decay

Using a sample of approximately one billion $J/\psi$ events collected by the BESIII detector, this paper reports the first observation of the $\eta_c \to K^0 \bar{K}^0$ decay and provides its measured branching fractions considering both constructive and destructive interference scenarios.

The Gist

The Mystery of the "Forbidden" Dance: A Simple Guide to the $\eta_c \to \Xi^0\bar{\Xi}^0$ Discovery

Imagine you are watching a professional ballroom dance competition. There is a very strict rulebook called pQCD (the "Rulebook of Physics"). According to this rulebook, a specific dancer—let’s call him $\eta_c$ (the Pseudoscalar)—is physically incapable of performing a certain move: a high-speed spin with a partner called the $\Xi^0\bar{\Xi}^0$ (the Baryon Pair).

The rulebook says that because of the way $\eta_c$ is built, the laws of "helicity" (which you can think of as the direction a dancer is spinning) should make this specific dance move impossible. If the rulebook is right, the music should play, but the dancers should just stand there, frozen.

But recently, scientists at the BESIII experiment caught them doing the dance anyway.

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1. The "Forbidden" Dance (The Scientific Problem)

In the world of subatomic particles, there is a principle called the Helicity Selection Rule (HSR). It’s like a cosmic law of etiquette. It predicts that certain particles shouldn't be able to decay (transform) into certain other particles because their "spins" don't line up correctly.

For years, physicists have been scratching their heads because they keep seeing these "forbidden" decays happening in real life. It’s like seeing a magician perform a trick that the laws of physics say shouldn't be possible.

2. The Discovery (What Happened?)

Using a massive particle collider in China (the BEPCII), scientists watched billions of $J/\psi$ particles. They were looking for a very specific, rare event: a $J/\psi$ particle turning into a photon (light) and an $\eta_c$ particle, which then immediately transforms into a pair of $\Xi^0$ particles.

They found it. This is the first time anyone has ever observed this specific transformation. It’s like finding a footprint of a creature that everyone thought was a myth.

3. Why Does This Matter? (The "Why Should I Care?" Part)

If the "Rulebook of Physics" (pQCD) says this dance is impossible, but we see it happening, it means one of two things:

1. The rulebook is incomplete.
2. There is a "secret mechanism" helping the dancers move.

The paper suggests a "secret mechanism" called the Intermediate Meson Loop (IML).

The Analogy: Imagine a dancer trying to cross a wide, slippery gap in the floor. According to the rules, they shouldn't be able to jump it. However, if they use a temporary "bridge" made of invisible stepping stones that appear for just a split second, they can make it across. In physics, these "stepping stones" are virtual particles (charmed mesons) that appear and disappear, allowing the $\eta_c$ to bypass the strict rules and complete the dance.

4. The Results (The Fine Print)

The scientists measured exactly how often this "forbidden" dance happens (the branching fraction). They found that the dance happens much more frequently than the old rules predicted.

They also had to deal with a bit of "interference." Imagine two different bands playing at the same time in a room. Sometimes the music blends together beautifully (constructive interference), and sometimes the notes clash and cancel each other out (destructive interference). Because they didn't know which one was happening, they provided two different mathematical answers, both of which confirm that the dance is definitely happening.

Summary in a Nutshell

• The Rule: Physics says particle $\eta_c$ shouldn't be able to turn into $\Xi^0\bar{\Xi}^0$.
• The Reality: We saw it happen!
• The Lesson: Our understanding of the "rules" of the subatomic world is still evolving. There are hidden "bridges" (mechanisms) in nature that allow particles to do things we once thought were impossible.

Technical Summary

Technical Summary: First Observation of the $\eta_c \to \Xi^0 \bar{\Xi}^0$ Decay

1. Problem and Motivation

The study addresses a long-standing puzzle in Quantum Chromodynamics (QCD) regarding the Helicity Selection Rule (HSR). According to perturbative QCD (pQCD), the HSR predicts that the decay of the $0^{-+}$ pseudoscalar charmonium state ($\eta_c$) into baryon–antibaryon ($B\bar{B}$) pairs should be forbidden due to quark helicity conservation.

However, previous experimental measurements of other $\eta_c$ decays have consistently shown non-zero branching fractions comparable to those of $J/\psi$ decays, contradicting pQCD predictions. While various theoretical models (e.g., quark-diquark, color-octet mechanism, and Intermediate Meson Loop models) have been proposed to explain this violation, they suffer from large quantitative uncertainties. To resolve these discrepancies, it is critical to observe additional "forbidden" decay channels. This paper focuses on the $\eta_c \to \Xi^0 \bar{\Xi}^0$ decay, which is the isospin partner of the previously studied $\eta_c \to \Xi^- \bar{\Xi}^+$ decay.

2. Methodology

The analysis was performed by the BESIII Collaboration using a massive data sample of $(10087 \pm 44) \times 10^6$ $J/\psi$ events collected at the BEPCII collider.

• Production Mechanism: Since $\eta_c$ cannot be produced directly in $e^+e^-$ annihilation, the researchers utilized the radiative decay process $J/\psi \to \gamma \eta_c$.
• Reconstruction Chain: The signal was reconstructed through the decay chain:
  $J/\psi \to \gamma \eta_c, \quad \eta_c \to \Xi^0 \bar{\Xi}^0, \quad \Xi^0 \to \Lambda \pi^0, \quad \bar{\Xi}^0 \to \bar{\Lambda} \pi^0, \quad \Lambda \to p \pi^-, \quad \bar{\Lambda} \to \bar{p} \pi^+, \quad \pi^0 \to \gamma \gamma$.
  The final state consists of $\gamma \gamma \gamma \gamma \gamma p \bar{p} \pi^+ \pi^-$.
• Event Selection:
  • Charged tracks were required to satisfy specific polar angle conditions and momentum thresholds to distinguish protons from pions.
  • A four-constraint (4C) kinematic fit was applied to the $\gamma \Lambda \bar{\Lambda} \pi^0 \pi^0$ hypothesis to ensure energy-momentum conservation.
  • A two-dimensional sideband analysis was used to estimate non-$\Xi^0 \bar{\Xi}^0$ backgrounds.
• Signal Extraction: The signal yield was extracted via an unbinned maximum-likelihood fit to the $M(\Xi^0 \bar{\Xi}^0)$ invariant mass distribution. Crucially, the fit accounted for the interference between the resonant process ($J/\psi \to \gamma \eta_c \to \gamma \Xi^0 \bar{\Xi}^0$) and the non-resonant process ($J/\psi \to \gamma \Xi^0 \bar{\Xi}^0$).

3. Key Contributions

• First Observation: This paper reports the first experimental observation of the $\eta_c \to \Xi^0 \bar{\Xi}^0$ decay.
• Interference Modeling: The study provides a sophisticated treatment of the interference phase ($\phi$) and the strength of the non-resonant component ($\alpha$), which is essential for accurate branching fraction measurements in charmonium decays.
• Isospin Symmetry Testing: By measuring this channel, the authors provide the necessary data to test isospin symmetry by comparing the results with the $\eta_c \to \Xi^- \bar{\Xi}^+$ channel.

4. Results

The fit yielded two possible solutions due to the nature of the interference: constructive and destructive.

• Branching Fractions for $\eta_c \to \Xi^0 \bar{\Xi}^0$:
  • Destructive Interference: $\mathcal{B}(\eta_c \to \Xi^0 \bar{\Xi}^0) = (1.33 \pm 0.03_{\text{stat}} \pm 0.18_{\text{syst}}) \times 10^{-3}$
  • Constructive Interference: $\mathcal{B}(\eta_c \to \Xi^0 \bar{\Xi}^0) = (1.63 \pm 0.04_{\text{stat}} \pm 0.21_{\text{syst}}) \times 10^{-3}$
• Statistical Significance: The significance of the $\eta_c$ signal exceeds $30\sigma$.
• Isospin Ratio: The ratio $\mathcal{B}(\eta_c \to \Xi^0 \bar{\Xi}^0) / \mathcal{B}(\eta_c \to \Xi^- \bar{\Xi}^+)$ was found to be approximately $1.5$, which is consistent with isospin symmetry expectations within $2\sigma$.

5. Significance

The results are highly significant for several reasons:

1. Validation of HSR Violation: The measured branching fractions are much larger than the predictions of the pQCD helicity selection rule, confirming that the rule is indeed violated in these decays.
2. Theoretical Discrimination: The results are compatible with the Intermediate Meson Loop (IML) model predictions ($(0.63 \sim 1.25) \times 10^{-3}$) but are substantially larger than the quark–diquark model predictions ($\approx 1.46 \times 10^{-4}$). This provides a critical benchmark for refining theoretical models of non-perturbative QCD.
3. Improved Precision: The study suggests that previous measurements may have underestimated branching fractions by failing to account for the interference between the $\eta_c$ resonance and non-resonant backgrounds.