⚛️ phenomenology

Identifying $\Sigma(1380)$ and $\Sigma(1430)$ in the $J/\psi \to \Lambda \pi \bar{\Sigma}$ reaction

This study investigates the $J/\psi \to \Lambda \pi \bar{\Sigma}$ reaction to identify low-lying $\Sigma^+$ states, confirming the $\Sigma(1385)$ and $\Sigma(1430)$ while finding that the necessity of the predicted $\Sigma(1380)$ state depends on whether $\pi\bar{\Sigma}$ interactions are included in the analysis.

Original authors: Wen-Tao Lyu, Eulogio Oset, De-Min Li, En Wang

Published 2026-07-03

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CC BY 4.0

Original authors: Wen-Tao Lyu, Eulogio Oset, De-Min Li, En Wang

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 bustling, chaotic construction site. In this paper, the authors are acting like detectives trying to identify specific "workers" (particles) that show up during a very specific demolition event: the decay of a heavy particle called the J/ψ into a trio of lighter particles: a Lambda ( $\Lambda$ ), a pion ( $\pi$ ), and an anti-Sigma ( $\bar{\Sigma}$ ).

The main goal of the investigation is to find two specific, hard-to-spot workers: the $\Sigma(1430)$ and the $\Sigma(1380)$ . These are unstable, short-lived particles that are notoriously difficult to see because they are often hidden in the shadows of a much louder, more dominant worker: the $\Sigma(1385)$ .

Here is the story of their investigation, broken down into simple steps:

1. The Problem: A Crowded Room

When the J/ψ decays, it creates a mess of particles. If you look at the energy of the Lambda and the pion together, you see a huge, loud peak. This is the $\Sigma(1385)$ . It's like a rock star screaming on stage; everyone hears it, and it drowns out the quiet whispers of the other particles.

The scientists suspect that hidden in the "low energy" corner of this crowd are two other particles:

$\Sigma(1430)$ : A particle predicted by theory and recently spotted by the Belle collaboration.
$\Sigma(1380)$ : A "ghost" particle that many previous studies claimed was necessary to explain data from other experiments, but which has never been clearly seen.

2. The First Clue: Looking at Just One Pair

In their first attempt, the authors looked at the data by only focusing on the relationship between the Lambda and the pion (ignoring the third particle, the anti-Sigma).

The Analogy: Imagine listening to a song and only focusing on the bass guitar.
The Result: When they did this, the loud rock star ( $\Sigma(1385)$ ) was there, but the music sounded "thin" at the low end. There was a gap in the sound that didn't fit the theory.
The Hypothesis: To fill that gap, they tried adding the $\Sigma(1380)$ to the mix. Suddenly, the music fit perfectly! The data looked great. They also saw a tiny hint of the $\Sigma(1430)$ .
The Trap: It looked like they had found the ghost ( $\Sigma(1380)$ ). But this was a trap. They were only looking at half the picture.

3. The Second Clue: The Full Orchestra

The authors realized that in the real world, the particles don't just interact in pairs; they interact in a complex web. The pion and the anti-Sigma also talk to each other, and this conversation affects the sound of the whole band.

The Analogy: They decided to listen to the entire orchestra (Lambda + Pion + Anti-Sigma) instead of just the bass. They included the "rescattering" effects—essentially, how the particles bounce off each other before flying away.
The Result: When they added this full context, the "missing sound" at the low end disappeared. The gap was filled not by the ghost particle ( $\Sigma(1380)$ ), but by the natural interaction of the other particles they were already watching.
The Twist: The "need" for the $\Sigma(1380)$ vanished. The data could be explained perfectly well without it. The "ghost" was just a mirage created by looking at the wrong angle.

4. The Verdict

The paper concludes with a very specific finding:

On the $\Sigma(1380)$ : In this specific reaction ( $J/\psi \to \Lambda\pi\bar{\Sigma}$ ), there is no evidence that the $\Sigma(1380)$ exists. The data that previously seemed to require it can be explained by the complex interactions of the other particles. The authors warn that just because a particle seems necessary in one experiment doesn't mean it's actually there; sometimes, you just need to look at the whole picture.
On the $\Sigma(1430)$ : They did find a small, faint signal for this particle, consistent with what the Belle experiment found. However, it's so small that they can't claim a definitive discovery yet; they just say, "Keep looking, it might be there."

Summary in a Nutshell

The authors tried to find a "ghost" particle ( $\Sigma(1380)$ ) in a noisy crowd.

First look: They thought they found it because the crowd sounded incomplete without it.
Second look: They realized the crowd was actually complete because the other people were talking to each other in a way they hadn't considered.
Conclusion: The ghost isn't needed to explain this specific event. The paper serves as a warning to other scientists: Don't jump to conclusions about new particles until you've checked every possible interaction. Sometimes, what looks like a new discovery is just a misunderstanding of how the old ones behave.

Technical Summary: Identifying $\Sigma(1380)$ and $\Sigma(1430)$ in the $J/\psi \to \Lambda\pi\bar{\Sigma}$ Reaction

Problem Statement
The existence and properties of low-lying $\Sigma^*$ baryon states, specifically the $\Sigma(1430)$ ( $J^P = 1/2^-$ ) and the more elusive $\Sigma(1380)$ ( $J^P = 1/2^-$ ), remain subjects of continuous debate. While the $\Sigma(1430)$ has been theoretically predicted via chiral unitary approaches and recently observed by the Belle Collaboration in $\Lambda_c^+$ decays, the $\Sigma(1380)$ is harder to identify due to the overwhelming dominance of the nearby $\Sigma(1385)$ ( $J^P = 3/2^+$ ) in $\pi\Lambda$ mass distributions. Previous analyses of various reactions (e.g., $K^-p$ , $\Lambda_c^+ \to \eta\pi\Lambda$ ) have claimed that the inclusion of a $\Sigma(1380)$ resonance is necessary to reproduce experimental data, particularly in the low-energy region of the $\pi\Lambda$ invariant mass spectrum. This work investigates whether the $J/\psi \to \Lambda\pi\bar{\Sigma}$ reaction, measured by the BESIII Collaboration, requires the $\Sigma(1380)$ to explain the low-energy $\pi^+\Lambda$ mass distribution, or if other dynamical mechanisms can account for the observed strength.

Methodology
The authors analyze the $J/\psi \to \Lambda\pi^+\bar{\Sigma}^-$ decay using a formalism that treats the $J/\psi$ as an $SU(3)$ singlet in the $u, d, s$ quark sector. The analysis proceeds in two distinct stages:

$\pi\Lambda$ Interaction Only: Initially, the study considers only the final state interaction (FSI) between the $\pi^+$ and $\Lambda$ . The amplitude is constructed to include tree-level contributions and resonant terms for the $\Sigma(1385)$ (P-wave), $\Sigma(1430)$ (S-wave), and $\Sigma(1380)$ (S-wave). The differential decay rate is calculated and fitted to the BESIII $\pi^+\Lambda$ mass distribution data.
Inclusion of $\pi\bar{\Sigma}$ Interaction: In the second, more comprehensive step, the authors incorporate the $\pi\bar{\Sigma}$ $π \overset{ˉ}{Σ}$ interaction and other coupled channels (such as $\bar{K}N$ $\overset{ˉ}{K} N$ , $\eta\Lambda$ $η Λ$ , etc.) that can rescatter into the $\pi\bar{\Sigma}$ $π \overset{ˉ}{Σ}$ final state. This is achieved using a formalism derived from chiral unitary approaches, where the $J/\psi$ $J / ψ$ decays into a baryon-antibaryon-meson trio ( $\Lambda\bar{\Sigma}\pi$ $Λ \overset{ˉ}{Σ} π$ ) via two distinct $SU(3)$ structures ( $\langle \bar{B}BP \rangle$ $⟨ \overset{ˉ}{B} B P ⟩$ and $\langle \bar{B}PB \rangle$ $⟨ \overset{ˉ}{B} P B ⟩$ ). The calculation includes:
- Tree-level production.
- Rescattering loops involving intermediate meson-baryon states ( $M\bar{B}$ ).
- Interference terms between different production amplitudes ( $t_1, t_2, t_3$ ), specifically noting that interference between the $\pi\Lambda$ resonant terms and the $\pi\bar{\Sigma}$ rescattering terms does not vanish upon integration over the angular variables.

Key Results

Analysis with $\pi\Lambda$ Interaction Only: When fitting the BESIII data considering only the $\pi\Lambda$ interaction, the $\Sigma(1385)$ peak is well reproduced. However, the model fails to account for the "missing strength" in the low-energy region of the $\pi^+\Lambda$ spectrum. Introducing a $\Sigma(1380)$ resonance significantly improves the fit, and adding a small $\Sigma(1430)$ contribution further refines the agreement with the data. This initial result mimics findings from other reactions that claim the necessity of the $\Sigma(1380)$ .
Analysis with $\pi\bar{\Sigma}$ Interaction: When the $\pi\bar{\Sigma}$ $π \overset{ˉ}{Σ}$ interaction and coupled channels are included, the conclusion changes drastically. The rescattering contributions from the $\pi\bar{\Sigma}$ $π \overset{ˉ}{Σ}$ system, along with interference terms, provide sufficient strength to reproduce the low-energy $\pi^+\Lambda$ $π^{+} Λ$ spectrum without invoking the $\Sigma(1380)$ $Σ (1380)$ .
- The fit to the BESIII data is achieved with high quality using only the $\Sigma(1385)$ and the $\pi\bar{\Sigma}$ dynamics.
- The inclusion of the $\Sigma(1380)$ is no longer required; its contribution disappears as a necessity when the full dynamics are considered.
- A small contribution from the $\Sigma(1430)$ remains compatible with the data but is not statistically significant based on the current single data point in that region.
Robustness: The conclusion that the $\Sigma(1380)$ is unnecessary is robust against variations in the ratio of the $SU(3)$ coupling parameters ( $\tilde{A}/\tilde{B}$ ), which were varied from 0.3 to 3.0 without altering the qualitative outcome.

Significance and Claims
The paper claims that the $J/\psi \to \Lambda\pi\bar{\Sigma}$ reaction cannot be used to support the existence or necessity of the $\Sigma(1380)$ resonance. The authors emphasize that the apparent need for the $\Sigma(1380)$ in previous studies of this reaction channel (when analyzed with limited dynamics) was an artifact of neglecting the $\pi\bar{\Sigma}$ interaction and coupled channel effects.

The primary significance of this work is methodological: it serves as a warning that claims regarding the necessity of specific resonances (like the $\Sigma(1380)$ ) based on experimental data must be treated with caution. Subtle dynamical details, such as final state interactions in coupled channels and interference effects, can fundamentally alter the interpretation of low-energy spectral strength. While the authors do not deny the existence of the $\Sigma(1380)$ in other contexts, they demonstrate that in this specific reaction, the data can be fully explained without it, suggesting that previous claims of its necessity in similar analyses may require re-evaluation.

1. The Problem: A Crowded Room

2. The First Clue: Looking at Just One Pair

3. The Second Clue: The Full Orchestra

4. The Verdict

Summary in a Nutshell

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