Observation of the Exotic State $\pi_{1}(1600)$ in $\psi(2S)\rightarrow\gamma\chi_{c1},\chi_{c1}\rightarrow\pi^{+}\pi^{-}\eta'$

Using a dataset of 2.7 billion $\psi(2S)$ events collected by the BESIII detector, researchers observed the exotic $J^{PC}=1^{-+}$ state $\pi_1(1600)$ in the decay $\chi_{c1}\rightarrow\pi^+\pi^-\eta'$ with a statistical significance exceeding $21\sigma$, determining its mass, width, and branching fraction product.

The Gist

Imagine the universe is a giant, cosmic Lego set. For decades, physicists have been building structures using two main types of bricks: quarks. They figured out that you can snap two quarks together to make a "meson" (like a car), or three quarks to make a "baryon" (like a truck). This was the standard rulebook for how matter is built.

But the rulebook of the universe (a theory called Quantum Chromodynamics, or QCD) hinted that there might be other, stranger ways to snap these bricks together. It suggested the existence of "hybrid" particles—structures where the quarks are glued together not just by the usual forces, but by a burst of pure energy (gluons) acting like a third, active brick. These hybrids would have "exotic" properties that normal Lego structures simply can't have.

For years, scientists have been hunting for one specific hybrid: a particle called $\pi_1(1600)$. It's like looking for a specific, mythical creature in a dense forest. Previous sightings were blurry, or people argued they were just tricks of the light (analysis errors).

The Big Hunt: The BESIII Detector

Enter the BESIII experiment in Beijing. Think of the BESIII detector as a massive, ultra-high-speed 360-degree security camera system sitting inside a particle accelerator.

The scientists didn't just look for the particle; they created a factory to make it. They smashed electrons and positrons together to create a heavy particle called the $\psi(2S)$. This particle is unstable and immediately decays (breaks apart) into a photon (a particle of light) and a $\chi_{c1}$ particle.

The $\chi_{c1}$ is the real star of the show. It's like a heavy, unstable bomb that explodes into a shower of smaller particles: two pions ($\pi^+ \pi^-$) and an $\eta'$ (eta-prime) meson.

The Detective Work: Finding the Ghost

The problem is that when the $\chi_{c1}$ explodes, it doesn't always go straight to the final pieces. Sometimes, it creates a temporary, fleeting "ghost" in the middle of the explosion. The scientists suspected that this ghost was the $\pi_1(1600)$.

Here is the analogy: Imagine you are at a party. You see a group of people (the final particles) dancing. You suspect that just before they started dancing, a specific, invisible DJ (the $\pi_1(1600)$) spun a record that caused them to dance that way. You can't see the DJ, but you can analyze the dance moves to prove the DJ was there.

The team analyzed 2.7 billion of these particle collisions. They used a sophisticated mathematical technique called Partial Wave Analysis (PWA). Think of PWA as a way to take a chaotic, noisy recording of a party and filter out the background chatter to isolate the specific rhythm of the DJ's music.

The Discovery

After sifting through the noise, they found a clear signal.

1. The "Exotic" Signature: The particles were dancing in a way that is mathematically impossible for normal quark combinations. They had a specific "spin" and "parity" (quantum numbers) of $1^{-+}$. In the Lego analogy, this is like finding a structure that requires a brick to be both "up" and "down" at the same time. Normal bricks can't do that; only the exotic "hybrid" bricks can.
2. The Confidence: The signal was so strong that the chance of it being a random fluke was less than one in a trillion. In scientific speak, they achieved a significance of 21 sigma. (In the world of particle physics, 5 sigma is usually enough to claim a discovery; 21 is like finding a needle in a haystack and then finding the same needle in 20 other haystacks simultaneously).
3. The Identity: They measured the mass and "width" (how long it lives) of this ghost. It weighed about 1828 MeV/c² (roughly twice the mass of a proton) and existed for a tiny fraction of a second before vanishing.

Why Does This Matter?

This isn't just about finding a new particle; it's about proving the existence of a new type of matter.

• Proving the Theory: It confirms that the "gluon glue" can act as a structural component, not just a binding agent. It proves that the universe allows for these exotic hybrid states.
• The "Hybrid" Family: The $\pi_1(1600)$ is likely the first confirmed member of a family of hybrid mesons. Finding it helps physicists understand the "dark matter" of the strong force (the force that holds atomic nuclei together).
• The Puzzle: The paper also mentions a similar particle, $\eta_1(1855)$, found recently. Scientists are now asking: Are these two particles cousins? Do they belong to the same "family tree" of exotic matter?

The Bottom Line

The BESIII collaboration didn't just find a new particle; they found a new kind of building block in the universe. By watching how billions of particles exploded and danced, they proved that nature has a more complex and colorful Lego set than we ever imagined. The $\pi_1(1600)$ is no longer a myth; it's a confirmed resident of the subatomic world, waiting for us to learn more about its strange, exotic nature.

Technical Summary

1. Problem and Scientific Context

• Theoretical Background: Within the Standard Model, hadrons are traditionally classified as quark-antiquark ($q\bar{q}$) mesons or three-quark ($qqq$) baryons. Quantum Chromodynamics (QCD) predicts the existence of "exotic" hadrons, such as hybrids (containing valence quarks and excited gluonic degrees of freedom), glueballs, and multiquark states.
• The Target: A specific class of exotic hybrids is predicted to have quantum numbers $J^{PC} = 1^{-+}$, which are forbidden for conventional $q\bar{q}$ mesons. Lattice QCD and phenomenological models predict the lightest hybrid meson with these quantum numbers to have a mass between 1.7 and 2.1 GeV/$c^2$.
• The Candidate: The $\pi_1(1600)$ is a long-standing candidate for this $1^{-+}$ hybrid state. Previous observations were primarily in diffractive production processes, which suffer from analysis artifacts and background complexities.
• The Gap: While the CLEO collaboration found evidence for an exotic $P$-wave $\pi\eta'$ amplitude in $\chi_{c1} \to \pi^+\pi^-\eta'$, they could not exclude non-resonant interactions. A definitive observation and spin-parity determination in a clean environment (charmonium decay) with higher statistics were required to confirm the resonant nature of the $\pi_1(1600)$.

2. Methodology

• Data Source: The analysis utilized a dataset of $(2712.4 \pm 14.3) \times 10^6$ $\psi(2S)$ events collected by the BESIII detector at the BEPCII collider.
• Reaction Chain: The study focused on the decay chain:
  $$\psi(2S) \to \gamma \chi_{c1}$$
  $$\chi_{c1} \to \pi^+ \pi^- \eta'$$
  Followed by two $\eta'$ decay modes:
  1. $\eta' \to \gamma \pi^+ \pi^-$
  2. $\eta' \to \eta \pi^+ \pi^- \to \gamma \gamma \pi^+ \pi^-$
• Event Selection:
  • Charged tracks were reconstructed in the MDC with strict kinematic constraints.
  • Photons were identified in the EMC with energy thresholds and timing cuts.
  • Kinematic Fits: A 4-constraint (4C) kinematic fit was applied to enforce energy-momentum conservation.
  • Veto Cuts: Events were rejected if they contained $\pi^0$ or $\eta$ backgrounds (via invariant mass vetoes) or if they matched the $J/\psi$ mass (to suppress $J/\psi$ backgrounds).
  • Final Sample: 24,577 candidates for the $\eta' \to \gamma \pi^+ \pi^-$ channel and 12,952 for the $\eta' \to \pi^+ \pi^- \eta$ channel.
• Analysis Technique:
  • Partial Wave Analysis (PWA): Performed using the GPUPWA framework.
  • Model: The signal amplitudes were modeled using the isobar model with covariant tensor formalism. The decay was treated as quasi-sequential two-body decays ($\chi_{c1} \to Y \eta'$ or $\chi_{c1} \to Z \pi^\mp$).
  • Fitting: An unbinned maximum likelihood fit was performed on the combined data of both $\eta'$ decay modes.
  • Background Handling: Non-$\eta'$ backgrounds were estimated using mass sidebands and subtracted in the likelihood fit.
  • Resonance Parametrization: The $\pi_1(1600)$ was modeled using a relativistic Breit-Wigner (BW) function with a mass-dependent width. Systematic uncertainties were evaluated by varying background normalizations, resonance parameters, and alternative parametrizations (e.g., constant width).

3. Key Contributions

• First Observation in Charmonium: This is the first observation of the $\pi_1(1600)$ in charmonium decays, providing a cleaner environment than previous diffractive production studies.
• Spin-Parity Determination: The analysis definitively determined the quantum numbers of the observed state to be $J^{PC} = 1^{-+}$, confirming its exotic nature.
• Robust Statistical Significance: The observation achieved a statistical significance of over $21\sigma$, far exceeding the threshold for discovery.
• Phase Motion Evidence: The analysis demonstrated a significant phase motion ($>11\sigma$) consistent with a resonant state, distinguishing it from non-resonant background.

4. Results

• Mass and Width:
  • Using a mass-dependent width BW function:
    • Mass: $1828 \pm 8 \text{ (stat)} ^{+11}_{-33} \text{ (syst)}$ MeV/$c^2$.
    • Width: $638 \pm 26 \text{ (stat)} ^{+35}_{-86} \text{ (syst)}$ MeV.
  • Using a constant width BW function (alternative analysis):
    • Mass: $1675 \pm 9 \text{ (stat)} ^{+32}_{-32} \text{ (syst)}$ MeV/$c^2$.
    • Width: $443 \pm 15 \text{ (stat)} ^{+18}_{-56} \text{ (syst)}$ MeV.
  • Note: Both parametrizations yield consistent pole positions, indicating physical equivalence despite parameter differences.
• Branching Fractions:
  The product of branching fractions was determined as:
  $$\mathcal{B}(\chi_{c1} \to \pi_1(1600)^\pm \pi^\mp) \times \mathcal{B}(\pi_1(1600)^\pm \to \pi^\pm \eta') = (4.30 \pm 0.14 \text{ (stat)} ^{+1.04}_{-1.03} \text{ (syst)}) \times 10^{-4}$$
• Pole Position: The pole position was determined to be approximately $(1690 \pm 16 + 36_{-44}) - i(217 \pm 5 + 7_{-19})$ MeV.
• Fit Quality: The PWA fit included other resonances ($a_0(980)\pi$, $f_2(1270)\eta'$, $X(2200)$, etc.) and showed excellent agreement with the data distributions (Dalitz plots and angular distributions), with $\chi^2/n_{bin}$ values indicating a good fit.

5. Significance

• Confirmation of Hybrid Meson: The observation of a $1^{-+}$ state with a mass consistent with Lattice QCD predictions ($\sim 1.7$ GeV/$c^2$) provides strong experimental evidence for the existence of hybrid mesons, a crucial missing piece in the QCD spectrum.
• Resolution of Previous Ambiguities: By utilizing the clean initial state of $e^+e^-$ annihilation and a large dataset, this study resolves previous ambiguities regarding the resonant nature of the $\pi_1(1600)$ seen in CLEO data.
• Future Directions: The results suggest that the $\pi_1(1600)$ and the recently observed isoscalar $\eta_1(1855)$ may form a $1^{-+}$ hybrid nonet. The paper calls for further searches in neutral channels (e.g., $\chi_{c1} \to \pi^0\pi^0\eta'$) to test isospin symmetry and confirm the C-parity of the state.

In summary, this paper represents a landmark achievement in hadron spectroscopy, definitively identifying the $\pi_1(1600)$ as an exotic hybrid meson through high-statistics partial wave analysis at BESIII.