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

Understand

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.