Observation of $\chi_{cJ}(J=0,1,2)\rightarrow p\bar{p}\eta\eta$

Using a sample of $(2712.4\pm14.3)\times10^6$ $\psi(3686)$ events collected by the BESIII detector, this study reports the first observation of the decays $\chi_{cJ}(J=0,1,2)\rightarrow p\bar{p}\eta\eta$ with statistical significances exceeding $5\sigma$ and determines their branching fractions while finding no evidence of resonant structures in the $p\bar{p}$ or $p\eta/\bar{p}\eta$ systems.

The Gist

Imagine the universe as a giant, high-speed particle accelerator, like a cosmic racetrack where tiny subatomic particles zoom around at nearly the speed of light. In this paper, the BESIII collaboration (a team of scientists from around the world) acted like detectives at this racetrack, looking for a very specific, rare, and previously unseen "traffic accident."

Here is the story of their discovery, broken down into simple concepts:

1. The Setup: The "Cosmic Factory"

The scientists used a machine called BEPCII in Beijing, China. Think of this machine as a massive factory that smashes electrons and positrons (the antimatter twin of an electron) together.

• The Product: When these particles smash, they sometimes create a heavy, short-lived particle called $\psi(3686)$. You can think of this particle as a "heavy parent" or a "super-excited atom."
• The Decay: This heavy parent doesn't last long. It almost immediately splits apart. Usually, it sheds a flash of light (a photon) and turns into a slightly lighter "child" particle called $\chi_{cJ}$.
• The Mystery: The scientists wanted to see what happens when these "child" particles ($\chi_{cJ}$) break apart again. Specifically, they were looking for a very specific breakup: turning into a proton, an anti-proton, and two eta particles (which are like unstable, short-lived cousins of pions).

2. The Challenge: Finding a Needle in a Haystack

The team had a massive dataset: over 2.7 billion of these "heavy parent" particles ($\psi(3686)$).

• The Analogy: Imagine you have a giant haystack containing 2.7 billion pieces of straw. You are looking for a specific, rare needle that breaks apart into four specific smaller pieces.
• The Noise: Most of the time, the particles break apart in boring, common ways. The scientists had to filter out billions of "wrong" events to find the few hundred "right" ones. They used a digital sieve (called a Monte Carlo simulation) to predict what the "needle" should look like and then scanned their data to match it.

3. The Discovery: "We Found It!"

After filtering through the billions of events, they found the pattern they were looking for.

• The Result: They observed the decay $\chi_{cJ} \to p\bar{p}\eta\eta$ for the first time in history.
• The Confidence: In science, you can't just say "we think we saw it." You need to be sure it's not a random glitch. The team calculated a "statistical significance" of 5 to 13 sigma.
  • The Metaphor: If you flip a coin and get heads 5 times in a row, it's luck. If you get heads 13 times in a row, it's suspicious. If you get it 13 times and the odds of it being a fluke are 1 in 3.5 billion, you can be absolutely certain you found something real. This is what "5 sigma" means in particle physics—it's the gold standard for a discovery.

4. What Did They Learn?

The scientists measured how often this happens (the branching fraction).

• The Numbers: They found that for every 100,000 times the $\chi_{c0}$ particle breaks apart, it does this specific breakup about 6 times. For the other two types ($\chi_{c1}$ and $\chi_{c2}$), it happens even less often (about 1 to 2 times per 100,000).
• The "Ghost" Hunt: The scientists also looked closely at the debris to see if there were any "ghosts" in the machine—meaning, did the particles form any temporary, exotic structures before breaking apart?
  • They looked for a famous mystery called the $X(p\bar{p})$ (a strange clump of matter that appears near the proton-antiproton threshold).
  • The Verdict: They found no evidence of this clump in this specific decay. It's like looking for a hidden room in a house and finding only empty space. This is actually useful information because it tells other physicists, "Hey, this mystery structure doesn't show up here, so maybe it's not as common as we thought."

5. Why Does This Matter?

You might ask, "Who cares about a proton breaking into an anti-proton and some other stuff?"

• Understanding the Rules: This helps us understand the Strong Force, the glue that holds the nucleus of an atom together. It's like studying how a Lego castle falls apart to understand how the bricks were connected in the first place.
• The "N(1535)" Puzzle: The paper mentions a specific excited proton called N(1535). Physicists have been puzzled by how often it turns into a proton and an eta particle. By studying these new decays, scientists hope to solve the mystery of why this particle behaves so strangely.
• New Physics: Every time we find a new way for particles to decay, it tests our current theories. If the numbers don't match our predictions, it could mean there is new, undiscovered physics waiting to be found.

Summary

The BESIII team acted like cosmic detectives. They sifted through 2.7 billion particle collisions, filtered out the noise, and confirmed the existence of a rare, previously unseen way for matter to transform. They didn't find the "ghosts" they were hunting for, but by proving exactly what happens (and what doesn't happen), they have given physicists a clearer map of the subatomic world.

Technical Summary

1. Problem and Motivation

The paper addresses two primary physics motivations within the realm of charmonium spectroscopy and hadron physics:

• First Observation: Prior to this study, the decays of the charmonium states $\chi_{c0}$, $\chi_{c1}$, and $\chi_{c2}$ into the four-body final state $p\bar{p}\eta\eta$ had never been observed. Establishing these branching fractions is crucial for understanding the decay dynamics of P-wave charmonia.
• Search for Exotic Structures: The authors aim to investigate the nature of the $X(p\bar{p})$ enhancement observed near the proton-antiproton threshold in other decays (e.g., $J/\psi \to \gamma p\bar{p}$). By studying the $p\bar{p}$ and $p\eta/\bar{p}\eta$ invariant mass spectra in $\chi_{cJ}$ decays, they seek to determine if similar resonant structures (potentially baryonium or multiquark states) exist in this channel.
• Excited Baryon Properties: The study also investigates the properties of the excited baryon $N(1535)$, which has a large branching fraction for $N(1535) \to p\eta$. Observing $N(1535)$ production in $\chi_{cJ}$ decays helps clarify its role in charmonium transitions.

2. Methodology

Data Sample:

• The analysis utilizes a data sample of $(2712.4 \pm 14.3) \times 10^6$ $\psi(3686)$ candidates collected by the BESIII detector at the BEPCII storage ring.
• The decay chain studied is the radiative transition: $\psi(3686) \to \gamma \chi_{cJ}$, followed by $\chi_{cJ} \to p\bar{p}\eta\eta$.
• Since $\eta \to \gamma\gamma$, the final state reconstructed is $p\bar{p}5\gamma$ (one photon from the initial transition, four photons from the two $\eta$ mesons).

Event Selection:

• Charged Tracks: Events must contain exactly two charged tracks identified as a proton ($p$) and an antiproton ($\bar{p}$) using $dE/dx$ and Time-of-Flight (TOF) information.
• Photon Selection: At least five photon candidates are required in the Electromagnetic Calorimeter (EMC) with specific energy thresholds (25 MeV in barrel, 50 MeV in end-cap) and timing cuts.
• Kinematic Fit: A 4-constraint (4C) kinematic fit is performed, constraining the total four-momentum of the final state to the colliding beam energy.
  • To suppress backgrounds from misidentified photon multiplicities (e.g., 4$\gamma$ or 6$\gamma$), the analysis requires $\chi^2(5\gamma p\bar{p}) < \chi^2(4\gamma p\bar{p})$ and $\chi^2(5\gamma p\bar{p}) < \chi^2(6\gamma p\bar{p})$.
  • To suppress $\pi^0$ backgrounds (e.g., $\chi_{cJ} \to p\bar{p}\pi^0\pi^0$), all $\gamma\gamma$ combinations are vetted against the $\pi^0$ mass window ($|M(\gamma\gamma) - m_{\pi^0}| > 15$ MeV/$c^2$).
• $\eta$ Reconstruction: The $\eta$ candidates are formed from four-photon combinations. The best combination is selected by minimizing $\Delta = \sqrt{(M(\gamma_1\gamma_2) - m_\eta)^2 + (M(\gamma_3\gamma_4) - m_\eta)^2}$.
• Signal Region Definition: The signal region is defined as $|M(\gamma\gamma) - m_\eta| < 20$ MeV/$c^2$ for both $\eta$ candidates. Sideband regions (SD1 and SD2) are used to estimate background contributions.

Background Estimation and Fitting:

• Continuum Background: Negligible, verified by analyzing off-resonance data samples at 3.650, 3.682, and 3.773 GeV.
• Peaking Background: Estimated using sideband events (SD1 and SD2) assuming a linear distribution for single-$\eta$ and non-$\eta$ peaking backgrounds.
• Fitting Strategy: A simultaneous fit is performed on the invariant mass distributions $M(p\bar{p}\eta\eta)$, $M(p\bar{p}\eta\gamma\gamma)$, and $M(p\bar{p}\gamma\gamma\gamma\gamma)$ for the signal and sideband regions.
  • Signal shape: Breit-Wigner (BW) function convolved with a Gaussian (detector resolution).
  • Background shape: 2nd-order Chebychev polynomial.

3. Key Contributions and Results

Observation of Decays:
The paper reports the first observation of $\chi_{cJ} \to p\bar{p}\eta\eta$ for all three states ($J=0, 1, 2$). The statistical significances are:

• $\chi_{c0}$: 13.4$\sigma$
• $\chi_{c1}$: 5.4$\sigma$
• $\chi_{c2}$: 9.6$\sigma$

Branching Fractions:
The branching fractions are determined as follows (statistical uncertainty $\pm$ systematic uncertainty):

• $\mathcal{B}(\chi_{c0} \to p\bar{p}\eta\eta) = (5.75 \pm 0.59 \pm 0.42) \times 10^{-5}$
• $\mathcal{B}(\chi_{c1} \to p\bar{p}\eta\eta) = (1.40 \pm 0.33 \pm 0.17) \times 10^{-5}$
• $\mathcal{B}(\chi_{c2} \to p\bar{p}\eta\eta) = (2.64 \pm 0.40 \pm 0.27) \times 10^{-5}$

Search for Intermediate Resonances:

• The authors examined the background-subtracted invariant mass distributions for $p\bar{p}$, $p\eta/\bar{p}\eta$, and $\eta\eta$.
• Result: No evident resonant structures were found in the $p\bar{p}$ or $p\eta/\bar{p}\eta$ systems. Specifically, no enhancement near the $p\bar{p}$ threshold (similar to the $X(p\bar{p})$ seen in $J/\psi$ decays) was observed in this channel.
• The distributions were consistent with phase-space simulations (PHSP) and signal Monte Carlo (MC) expectations, suggesting no dominant intermediate resonant states like $N(1535)$ or baryonium are significantly populated in these specific decays.

Systematic Uncertainties:
The total systematic uncertainties are approximately 7.3% ($\chi_{c0}$), 12.3% ($\chi_{c1}$), and 10.1% ($\chi_{c2}$). Major sources include photon reconstruction, tracking, kinematic fit efficiency, and the $\pi^0$ mass window definition.

4. Significance

• Completeness of Charmonium Decays: This work fills a gap in the experimental knowledge of $\chi_{cJ}$ decays, providing the first measurements for the $p\bar{p}\eta\eta$ channel.
• Constraints on Exotic Hadrons: The absence of the $X(p\bar{p})$ enhancement in $\chi_{cJ} \to p\bar{p}\eta\eta$ provides critical constraints on theoretical models. It suggests that the mechanism producing the $X(p\bar{p})$ in $J/\psi \to \gamma p\bar{p}$ may not be universal across all charmonium radiative decays or that the specific dynamics of $\chi_{cJ}$ decays suppress this structure.
• Baryon Spectroscopy: The lack of significant $N(1535)$ signals in the $p\eta$ subsystem implies that the production mechanism of excited baryons in $\chi_{cJ}$ decays differs from that in $\psi(3686) \to p\bar{p}\eta$, offering new data points for theoretical models of charmonium-baryon interactions.
• Methodological Benchmark: The rigorous use of sideband subtraction and simultaneous fitting across multiple mass spectra sets a standard for analyzing complex multi-body hadronic final states in charmonium physics.

In summary, this paper successfully observes three new decay modes of charmonium states, measures their branching fractions with high precision, and provides negative results for exotic resonant structures in these specific channels, thereby refining our understanding of strong interaction dynamics in the charmonium sector.