⚛️ phenomenology

Deciphering the nature of $X(2300)$ with the PACIAE model

Using the PACIAE 4.0 model, this study proposes that the newly observed $X(2300)$ particle could be a $P$ -wave $s\bar{s}$ meson, an $S$ -wave tetraquark, or a hadro-strangeonium state, and distinguishes these candidates by calculating their production rates and kinematic distributions in $e^+e^-$ collisions.

Original authors: Jian Cao, Wen-Chao Zhang, Jin-Peng Zhang, Bo Feng, An-Ke Lei, Zhi-Lei She, Hua Zheng, Dai-Mei Zhou, Yu-Liang Yan, Ben-Hao Sa

Published 2026-02-13

📖 4 min read🧠 Deep dive

CC BY 4.0

Original authors: Jian Cao, Wen-Chao Zhang, Jin-Peng Zhang, Bo Feng, An-Ke Lei, Zhi-Lei She, Hua Zheng, Dai-Mei Zhou, Yu-Liang Yan, Ben-Hao Sa

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the subatomic world as a massive, chaotic construction site. Usually, the "workers" (quarks) build standard houses: two-quark houses called mesons and three-quark houses called baryons. But sometimes, the workers get creative and build "exotic" structures, like four-quark apartments or five-quark mansions.

Recently, a team of scientists at the BESIII laboratory in China spotted a strange new "building" in the debris of particle collisions. They called it X(2300). It's a heavy, short-lived particle with a specific spin and shape (quantum numbers $1^{+-}$ ).

The big mystery? What exactly is this building made of? Is it a standard house with an extra floor? A four-quark apartment? Or something even weirder?

This paper is like a team of architectural detectives using a super-powerful computer simulation (called PACIAE) to test different blueprints to see which one fits the X(2300).

The Three Suspects (The Hypotheses)

The researchers proposed three different "architectural styles" for the X(2300) and simulated how often each would be built in their digital construction site:

The "Excited House" (Strangeonium):
- The Idea: Imagine a standard two-quark house (a strange quark and an anti-strange quark, $s\bar{s}$ ), but it's been excited, like a house with a bouncy floor or a weird roof. It's vibrating in a specific way (a "P-wave").
- The Simulation: They tried to glue two quarks together in the simulation to see if this "vibrating house" appeared.
The "Four-Quark Apartment" (Tetraquark):
- The Idea: This is a brand new type of building made of four bricks stuck together.
  - Type A: A mix of light bricks (up/down quarks) and heavy strange bricks ( $q\bar{q}s\bar{s}$ ).
  - Type B: A building made entirely of four strange bricks ( $s\bar{s}s\bar{s}$ ).
- The Simulation: They tried to glue four quarks together at once to see if these apartments formed.
The "Molecular Duo" (Hadro-strangeonium):
- The Idea: This is the most novel suggestion. Imagine two separate, sturdy houses (a $\phi$ meson and an $\eta'$ or $\eta$ meson) that are so attracted to each other they stick together like magnets to form a single unit. It's not a new building; it's a "house-hugging" scenario.
- The Simulation: They waited until the simulation finished building individual houses, then checked if a $\phi$ and an $\eta$ happened to stick together.

The Detective Work: How They Told Them Apart

Since they can't physically touch the X(2300) in the real world yet, the researchers looked at the "footprints" left behind in their simulation. They compared three key clues:

The Production Rate (How often they appear):
- The "Excited House" and the "Mixed Apartment" ( $q\bar{q}s\bar{s}$ ) were built very frequently (about 1 in 100,000 collisions).
- The "All-Strange Apartment" and the "Molecular Duo" were much rarer (about 1 in 1,000,000 collisions).
- Analogy: If you see a specific type of car at a traffic light 10 times more often than another, it's likely the more common model.
The Speed and Direction (Rapidity and Momentum):
- This is the most exciting part. The different "buildings" move differently when they are created.
- The Molecular Duo (the two houses hugging) tends to move with a bit more "oomph" sideways (higher transverse momentum). Why? Because it takes a lot of energy to push two heavy houses together and keep them stuck.
- The Apartment and Excited House (made of quarks glued directly) are more "compact" and tend to move more slowly sideways.
- Analogy: Imagine throwing a single tennis ball vs. throwing two tennis balls taped together. The taped pair might fly differently because of how they were thrown and how they interact with the air.

The Verdict

The paper doesn't say, "We found the answer!" Instead, it says, "Here is the map of what to look for."

The researchers are telling experimentalists at the BESIII lab:

"If you look at the real X(2300) particles and see that they are moving fast sideways and appear rarely, it's probably the Molecular Duo or the All-Strange Apartment. If you see them moving slower and appearing more often, it's likely the Excited House or the Mixed Apartment."

Why Does This Matter?

Understanding the X(2300) is like finding a new species of animal. Is it a dog with a weird coat, or is it a completely new animal?

If it's a Tetraquark, it proves that nature loves to build complex, multi-quark structures.
If it's a Molecular state, it teaches us how particles can stick together like magnets, which is crucial for understanding the "glue" (strong force) that holds the universe together.

By simulating these possibilities, the authors have given the scientific community a set of "checklists" (production rates and movement patterns) to finally solve the mystery of the X(2300).

1. Problem Statement

The BESIII collaboration recently observed an axial-vector particle, X(2300), in the $\psi(3686) \to \phi\eta\eta'$ process with quantum numbers $J^{PC} = 1^{+-}$ , a mass of 2316 MeV/ $c^2$ , and a width of 89 MeV. Theoretical interpretations of this state have been limited primarily to two hypotheses:

An excited strangeonium state ( $s\bar{s}$ ).
A fully strange tetraquark state ( $s\bar{s}s\bar{s}$ ).

However, these existing models do not fully explore other plausible configurations allowed by QCD dynamics, such as non-strange quark involvement via $U(1)$ anomaly couplings or bound states of mesons. The paper aims to systematically evaluate the production rates and kinematic characteristics of X(2300) under four distinct structural hypotheses to determine which configuration best aligns with theoretical expectations and future experimental data.

2. Methodology

The authors utilized the PACIAE 4.0 (Parton And Cascade In A Evolution) model, a parton and hadron cascade model, to simulate $e^+e^-$ collisions at a center-of-mass energy of $\sqrt{s} = 4.95$ GeV. The simulation workflow involved:

Initial State: Generation of $e^+e^-$ annihilation events using PYTHIA8, followed by gluon breaking-up and quark de-excitation.
Partonic Stage: Simulation of parton rescattering ( $2 \to 2$ ) using leading-order perturbative QCD cross-sections to generate the Final Partonic State (FPS).
Hadronization: Conversion of the FPS into hadrons via the Lund string fragmentation scheme, followed by hadronic rescattering ( $2 \to 2$ ) to reach kinetic freeze-out, generating the Final Hadronic State (FHS).
Coalescence Model (DCPC): The authors employed the Dynamically Constrained Phase-Space Coalescence (DCPC) model, inspired by quantum statistical mechanics, to form the X(2300) candidates:
- Excited Strangeonium ( $s\bar{s}$ ): Formed by coalescing an $s\bar{s}$ pair in the FPS.
- Tetraquarks ( $q\bar{q}s\bar{s}$ and $s\bar{s}s\bar{s}$ ): Formed by coalescing four constituent quarks in the FPS.
- Hadro-strangeonium ( $\phi\eta'/\phi\eta$ ): Formed by the recombination of constituent mesons ( $\phi$ and $\eta'/\eta$ ) in the FHS.
Spectral Classification: The orbital angular momentum ( $L$ ) was calculated in the rest frame of the candidate using the relation $l^{*2} = L(L+1)\hbar^2$ . Candidates were classified based on their $J^{PC}$ quantum numbers.

3. Key Contributions

Novel Hypotheses: For the first time, the paper proposes and simulates two new structural candidates for X(2300):
1. A $q\bar{q}s\bar{s}$ tetraquark state (where $q=u/d$ ), motivated by $U(1)$ anomaly couplings allowing non-strange quarks to interact with the $s\bar{s}$ component.
2. A hadro-strangeonium state, defined as a bound system of a strangeonium ( $\phi$ ) and a light meson ( $\eta$ or $\eta'$ ), analogous to hadro-charmonium states.
Comprehensive Spectral Analysis: The study rigorously classifies the candidates based on $J^{PC}=1^{+-}$ $J^{P C} = 1^{+-}$ , identifying them as:
- $P$ -wave $s\bar{s}$
- $S$ -wave $q\bar{q}s\bar{s}$ / $s\bar{s}s\bar{s}$
- $S$ -wave $\phi\eta'/\phi\eta$
  (Note: $D$ -wave configurations were discarded due to mass discrepancies and formation difficulty.)
First-Estimate Production Rates: The paper provides the first quantitative estimates of production yields for these specific configurations in $e^+e^-$ collisions.

4. Results

Production Yields:
- The $P$ -wave $s\bar{s}$ and $S$ -wave $q\bar{q}s\bar{s}$ states exhibit the highest production rates, on the order of $10^{-5}$ per event.
- The $S$ -wave $s\bar{s}s\bar{s}$ and $\phi\eta'/\phi\eta$ states have lower yields, on the order of $10^{-6}$ .
- Specifically, the $s\bar{s}s\bar{s}$ yield is approximately twice that of the $s\bar{s}$ state, while the $\phi\eta$ yield is higher than $\phi\eta'$ due to phase-space suppression of the heavier $\eta'$ .
Kinematic Distributions:
- Rapidity ( $y$ ): All configurations show a peak at mid-rapidity. The peak height follows the hierarchy: $q\bar{q}s\bar{s} > s\bar{s} > s\bar{s}s\bar{s} > \phi\eta > \phi\eta'$ , consistent with their production yields.
- Transverse Momentum ( $p_T$ ):
  - Compact states ( $s\bar{s}$ , $q\bar{q}s\bar{s}$ , $s\bar{s}s\bar{s}$ ) peak at $p_T \approx 0.3$ GeV/ $c$ .
  - The hadro-strangeonium states ( $\phi\eta'/\phi\eta$ ) peak at a significantly higher $p_T \approx 0.5$ GeV/ $c$ .
  - Physical Explanation: The higher $p_T$ for hadro-strangeonium arises because it requires the co-production of two heavy mesons ( $\phi$ and $\eta'/\eta$ ), necessitating substantial transverse momentum transfer from the parton shower. In contrast, compact tetraquarks/quarkonia form via direct quark recombination without the constraint of pre-existing heavy meson kinematics.

5. Significance

This work provides critical theoretical benchmarks for experimentalists at BESIII and future $e^+e^-$ colliders.

Discrimination Criteria: The distinct differences in production rates and, more importantly, the transverse momentum spectra offer a robust method to distinguish between the competing nature of X(2300).
- If X(2300) is observed with a $p_T$ peak near 0.5 GeV/ $c$ , it strongly supports the hadro-strangeonium hypothesis.
- If the peak is near 0.3 GeV/ $c$ with a yield around $10^{-5}$ , it favors the $q\bar{q}s\bar{s}$ or $s\bar{s}$ interpretations.
Theoretical Expansion: By introducing the $q\bar{q}s\bar{s}$ and hadro-strangeonium models, the paper broadens the search space for exotic hadrons beyond traditional tetraquark and meson classifications, suggesting that "molecular" or "hadro-" bound states may be more prevalent in the strange sector than previously assumed.