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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. Withstill sufficient freedom for model parameters, the $\Lambda(1405)$ and$\bar\Lambda(1405)$ resonances are generated by simultaneously taking the mesonbaryon and meson anti-baryon final state interactions into account. The$\pi\Sigma$ ($\pi\bar\Sigma$) invariant mass distributions peak around 1410MeV, which favors the assertion that the $\Lambda(1405)$ ($\bar\Lambda(1405)$)is a superposition of the two $\Lambda(1405)$ ($\bar\Lambda(1405)$) stateswhich dominantly couple to $\bar K N$ ($K\bar N$) and $\pi\Sigma$($\pi\bar\Sigma$), respectively. We also calculate the amplitude for isospinI=1 which gives hints on a possible I=1 baryon resonance in the energy regionof the $\Lambda(1405)$, which up to now has not been observed.Comment: 17 pages, 5 figures, version accepted for publication in Phys. Rev.

physical review. c. nuclear physics/physical review. c, nuclear physics

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