$\Lambda(1405)$ and $\bar\Lambda(1405)$ in $J/\psi$ four-body decays

We study the structure of the baryon resonances $\Lambda(1405)$ and $\bar\Lambda(1405)$ in $J/\psi$ four body decays $J/\psi\to \Sigma\bar \Sigma \pi\pi$ in the framework of a coupled channel chiral unitary approach. With still sufficient freedom for model parameters, the $\Lambda(1405)$ and $\bar\Lambda(1405)$ resonances are generated by simultaneously taking the meson baryon and meson anti-baryon final state interactions into account. The $\pi\Sigma$ ($\pi\bar\Sigma$) invariant mass distributions peak around 1410 MeV, which favors the assertion that the $\Lambda(1405)$ ($\bar\Lambda(1405)$) is a superposition of the two $\Lambda(1405)$ ($\bar\Lambda(1405)$) states which dominantly couple to $\bar K N$ ($K\bar N$) and $\pi\Sigma$ ($\pi\bar\Sigma$), respectively. We also calculate the amplitude for isospin I=1 which gives hints on a possible I=1 baryon resonance in the energy region of the $\Lambda(1405)$, which up to now has not been observed.