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

Abstract

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.

Comments: 17 pages, 5 figures, version accepted for publication in Phys. Rev. C