The chiral partner of the nucleon in the mirror assignment with global symmetry

We calculate the pion-nucleon scattering lengths a0(±) and the mass parameter m0, which describes the nucleon mass in the chirally restored phase for parity-doubled nucleons. This is done at tree-level in the framework of a linear sigma model with global chiral symmetry. We obtain m0=300-600 MeV when using the recent lattice results of T.Takahashi and T. Kunihiro. While a0(-) is in fair agreement with experimental data, a0(+) is too small because of the employed large mass of the sigma meson. This indicates the need of an additional scalar degree of freedom, such as a scalar tetraquark state with a mass of about 500 MeV. In this framework the very existence of a light tetraquark is responsible of the stability of nuclear matter.