Λ(1405)andΛ¯(1405)inJ∕ψfour-body decays

Abstract

We study the structure of the baryon resonances $\ensuremath{\Lambda}(1405)$ and $\overline{\ensuremath{\Lambda}}(1405)$ in $J∕\ensuremath{\psi}$ four-body decays $J∕\ensuremath{\psi}\ensuremath{\rightarrow}\ensuremath{\Sigma}\overline{\ensuremath{\Sigma}}\ensuremath{\pi}\ensuremath{\pi}$ in the framework of a coupled channel chiral unitary approach. With still sufficient freedom for model parameters, the $\ensuremath{\Lambda}(1405)$ and $\overline{\ensuremath{\Lambda}}(1405)$ resonances are generated by simultaneously taking the meson baryon and meson antibaryon final state interactions into account. The $\ensuremath{\pi}\ensuremath{\Sigma}\phantom{\rule{0.3em}{0ex}}(\ensuremath{\pi}\overline{\ensuremath{\Sigma}})$ invariant mass distributions peak around 1410 MeV, which favors the assertion that the $\ensuremath{\Lambda}(1405)\phantom{\rule{0.3em}{0ex}}[\overline{\ensuremath{\Lambda}}(1405)]$ is a superposition of the two $\ensuremath{\Lambda}(1405)\phantom{\rule{0.3em}{0ex}}[\overline{\ensuremath{\Lambda}}(1405)]$ states which dominantly couple to $\overline{K}N\phantom{\rule{0.3em}{0ex}}(K\overline{N})$ and $\ensuremath{\pi}\ensuremath{\Sigma}\phantom{\rule{0.3em}{0ex}}(\ensuremath{\pi}\overline{\ensuremath{\Sigma}})$, respectively. We also calculate the amplitude for isospin $I=1$ which gives hints of a possible $I=1$ baryon resonance in the energy region of the $\ensuremath{\Lambda}(1405)$, which up to now has not been observed.