Lambda(1405) poles obtained from pi0-Sigma0 photoproduction data

TL;DR

This paper develops a method to determine the positions of the two $ ext{Lambda}(1405)$ poles from photoproduction data, confirming their existence and properties consistent with chiral unitary models.

Contribution

It introduces a novel approach combining chiral dynamics and experimental data to extract the two $ ext{Lambda}(1405)$ poles from photoproduction reactions.

Findings

Identified two $ ext{Lambda}(1405)$ poles at 1385-68i MeV and 1419-22i MeV.

Validated the method by fitting experimental data with good accuracy.

Predicted cross sections for related reactions to support the pole analysis.

Abstract

We present a strategy to extract the position of the two $\Lambda(1405)$ poles from experimental photoproduction data measured recently at different energies in the $\gamma p \to K^+ \pi^0 \Sigma^0 $ reaction at Jefferson Lab. By means of a chiral dynamics motivated potential but with free parameters, we solve the Bethe Salpeter equation in the coupled channels $\bar K N$ and $\pi \Sigma$ in isospin I=0 and parameterize the amplitude for the photonuclear reaction in terms of a linear combination of the $\pi \Sigma \to \pi \Sigma$ and $\bar K N \to \pi \Sigma$ scattering amplitudes in I=0, with a different linear combination for each energy. Good fits to the data are obtained with some sets of parameters, by means of which one can also predict the cross section for the $K^- p \to \pi^0 \Sigma^0 $ reaction. These later results help us decide among the possible solutions. The result is that the different solutions lead to two poles similar to those found in the chiral unitary approach. With the best result we find the two $\Lambda(1405)$ poles at $1385-68i\mev$and $1419-22i\mev$.