Testing the nature of the $\Sigma^*(1430)$

TL;DR

This paper investigates whether the $ ext{Sigma}^*(1430)$ resonance is a non-molecular state by analyzing its couplings and properties, concluding that a largely non-molecular nature is unlikely given current experimental data.

Contribution

It provides a theoretical analysis of the $ ext{Sigma}^*(1430)$ state, exploring its possible non-molecular nature and implications for its observable properties.

Findings

Non-molecular interpretation predicts extremely narrow width incompatible with experiments.

Large molecular components are favored for the state to match observed properties.

Mismatches suggest the state is unlikely to be purely non-molecular.

Abstract

We study the feasibility of having the $\Sigma^*(1430)$ state, predicted within the chiral unitary approach and recently reported by the Belle Collaboration, as corresponding to a state of non-molecular nature. Starting from this assumption, since the state is observed in the $\pi \Lambda$ channel, we allow the coupling to this state and relate the coupling to $\bar K N$ and $\pi \Sigma$ using $SU(3)$ symmetry arguments. We find that it is possible to have such a state with negligible coupling to the molecular components with a bare mass of the state very close to the physical mass of the $\Sigma^*(1430)$. Yet, this has consequences on other observables, since the width obtained is extremely small and incompatible with the Belle observations, and it leads to abnormally large values of the $\bar K N$ effective range. Conversely, such mismatches do not appear for large values of the bare mass of the state, but in this case we observe that the state develops large molecular components. While one can rule out a largely non-molecular nature for this state, its properties and detailed nature will need further experimental developments which one can anticipate will be coming in the near future.