The Sigma(1380) and Sigma(1430) are both hypothetical negative-parity states with spin one half, and both remain contentious. The Sigma(1430) was predicted in the chiral unitary approach, where the interaction of mesons with baryons in coupled channels generates a cusp-like structure at the anti-K N threshold, or a slightly bound state depending on details of the input. That picture has been corroborated by further studies constrained by pi N and anti-K N data, and the Belle Collaboration recently reported the first clear evidence for the state, seeing a signal at the anti-K N threshold in the Lambda pi mass distributions of the Lambda_c decay into pi+ pi+ pi- Lambda, although the data cannot discriminate between a genuine resonance and a cusp.

The Sigma(1380) is even more elusive. Its mass sits close to that of the well-established Sigma(1385), a spin-three-halves state that dominates most pi Lambda mass distributions, making any weaker structure underneath extremely hard to isolate. Support for the Sigma(1380) has accumulated indirectly: it was invoked to improve fits to K- p to Lambda pi- pi+ data, to LEPS photoproduction data, to Lambda p to Lambda p pi0, and to several Lambda_c decay spectra, where its inclusion significantly improved the description of the low-energy pi Lambda region. Notably, the authors stress that the Sigma(1380) cannot be a meson-baryon molecule like the Sigma(1430), because the chiral unitary studies leave no room for an additional isospin-one, spin-one-half negative-parity state; some pentaquark configurations, however, could accommodate a mass near 1380 MeV.

The new work focuses on the J/psi decay into Lambda pi+ anti-Sigma-, for which the BESIII Collaboration has measured the pi+ Lambda mass distribution. The spectrum is dominated by a very strong Sigma(1385) peak, but the authors noticed two features: a hint of a very small contribution around 1430 MeV, and a tail at low invariant masses that deviates from a symmetric Breit-Wigner shape, hinting at extra strength in that region.

To model the decay, the team treated the J/psi as an SU(3) singlet in the light quarks and adopted a simplified P-wave coupling for producing the baryon-antibaryon pair, writing the amplitude in terms of the J/psi polarization vector dotted with the anti-Sigma momentum. The angular dependence was decomposed into spherical harmonics: the Sigma(1385) proceeds via P-wave, while a tree-level term and a possible Sigma(1430) signal both enter in S-wave. The Sigma(1430) mass and width were varied around 1430 MeV and 22 MeV, and the Sigma(1385) parameters were taken from the Review of Particle Physics.

In the first analysis, considering only the pi+ Lambda interaction, the Sigma(1385) peak was reproduced reasonably well but strength was missing at low invariant mass. Replacing the Sigma(1430) term by a Sigma(1380) resonance, with a mass of 1380 MeV and a width of 120 MeV drawn from earlier studies, produced a very good fit to the data, and adding both states filled the remaining gap around 1430 MeV. Quantitatively, including the Sigma(1380) reduced the chi-squared per degree of freedom by a factor of two, and the small Sigma(1430) contribution improved the description near 1430 MeV without changing the global chi-squared.

The turning point came when the authors included the pi anti-Sigma interaction, which had been neglected in the first pass. Using a formalism developed for the related J/psi decay into Lambda anti-Sigma0 eta, they built the full amplitude from two SU(3) singlet structures and allowed the produced meson-antibaryon pairs to rescatter into the pi+ anti-Sigma- final state through coupled channels including pi Sigma, eta Lambda, K N and K Xi. The rescattering amplitudes are S-wave, so only the Lambda-momentum piece of the production vertex feeds the loops, and the resulting terms interfere with the dominant Sigma(1385) contribution in a way that cannot be ignored.

The consequences were dramatic. With the pi anti-Sigma interaction and its coupled channels included, and with no Sigma(1380) or Sigma(1430) at all, the fit to the BESIII pi+ Lambda spectrum became good, and the chi-squared per degree of freedom dropped by more than a factor of two relative to the fit that had required the Sigma(1380). The conclusion proved robust: varying the ratio of the two SU(3) amplitudes over a wide range, from 0.3 to 3, always allowed a very good fit after adjusting only the normalization and the Sigma(1385) strength, so the result does not hinge on that parameter. Adding a small Sigma(1430) contribution improved the 1430 MeV region slightly, but only on the basis of a single data point, and it slightly worsened the agreement at higher masses while still beating the two-state fit by about a factor of two in chi-squared.

The authors explain the mechanism with a Dalitz-plot analysis: the pi anti-Sigma channel and its coupled partners generate antihyperon resonances, including the anti-Lambda(1380), anti-Lambda(1420) and anti-Lambda(1670), all of which influence the pi Lambda mass distribution in the analysed region. They also note that the individual Sigma(1380) and Sigma(1430) terms are extremely small on their own; it is interference with other terms that makes them appear sizeable, whereas the pi anti-Sigma final-state interaction by itself is quite large, with the good fit achieved through a smaller effective Sigma(1385) contribution.

The takeaway is a warning as much as a result. The study concludes that the J/psi to Lambda pi anti-Sigma reaction cannot be used to claim the need for a Sigma(1380) resonance, while explicitly stating that nothing is said about other reactions from which the state has been claimed. More broadly, the exercise shows that careful analysis is essential, since subtle effects and small contributions, such as final-state interactions that are easy to overlook, can flip conclusions about whether a resonance is required to explain data. The authors suggest that measurements with high statistics be performed to eventually reveal a clear signal of the Sigma(1430), which they expect to be small, as the Belle experiment already indicated.

Subject of Research: Theoretical analysis of excited Sigma baryon signals in the J/psi decay into Lambda, pion and anti-Sigma

Article Title: Identifying \(\Sigma (1380)\) and \(\Sigma (1430)\) in the \(J/\psi \rightarrow \Lambda \pi \bar{\Sigma }\) reaction

Article References: Lyu, W.-T., Oset, E., Li, D.-M., & Wang, E. (2026). Identifying $$\Sigma (1380)$$ and $$\Sigma (1430)$$ in the $$J/\psi \rightarrow \Lambda \pi \bar{\Sigma }$$ reaction. The European Physical Journal C, 86(10), Article 1235. https://doi.org/10.1140/epjc/s10052-026-16496-0

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16496-0

Keywords: Sigma(1380), Sigma(1430), J/psi decay, chiral unitary approach, BESIII, Belle, pi Lambda mass distribution, final-state interaction, baryon resonances, hadron physics, pentaquark, coupled channels