How to unravel the nature of the $\Sigma^*(1430) (1/2^-)$ state from correlation functions

Abstract

We calculate the correlation functions for the $\bar K^0 p, \pi^+ \Sigma^0, \pi^0 \Sigma^+, \pi^+ \Lambda$, and $\eta \Sigma^+$ states, which in the chiral unitary approach predict an excited $\Sigma^*(1/2^-)$ state at the $\bar K N$ threshold, recently observed by the Belle Collaboration. Once this is done, we tackle the inverse problem of seeing how much information one can obtain from these correlation functions. With the resampling method, one can determine the scattering parameters of all the channels with relative precision by means of the analysis in a general framework, and find a clear cusplike structure corresponding to the $\Sigma^*(1/2^-)$ in the different amplitudes at the $\bar{K}N$ threshold.