We investigate a linear sigma model with global chiral Uð2Þ R Â Uð2Þ L symmetry. The mesonic degrees of freedom are the standard scalar and pseudoscalar mesons and the vector and axial-vector mesons. The baryonic degrees of freedom are the nucleon, N, and its chiral partner, N Ã , which is usually identified with Nð1535Þ. The chiral partner is incorporated in the so-called mirror assignment, where the nucleon mass is not solely generated by the chiral condensate but also by a chirally invariant mass term, m 0 . The presence of (axial-) vector fields modifies the expressions for the axial-coupling constants of the nucleon, g N A , and its partner, g N Ã A . Using experimental data for the decays N Ã ! N and a 1 ! , as well as lattice results for g N Ã A we infer that in our model m 0 $ 500 MeV, i.e., an appreciable amount of the nucleon mass originates from sources other than the chiral condensate. We test our model by evaluating the decay N Ã ! N and the s-wave nucleon-pion scattering lengths a ðAEÞ 0 .

We investigate the role of a scalar tetraquark state for the description of nuclear matter within the parity doublet model in the mirror assignment. In the dilatation-invariant version of the model a nucleon-nucleon interaction term mediated by the lightest scalar tetraquark field naturally emerges. At nonzero density one has, beyond the usual chiral condensate, also a tetraquark condensate. The behavior of both condensates and the restoration of chiral symmetry at high density are studied. It is shown that this additional scalar degree of freedom affects non negligibly the properties of the medium.

In the framework of chiral model(s) based on the linear realization of chiral symmetry, we investigate the low-energy phenomenological properties of the nucleon and its chiral partner (identified with either N (1535) or N (1650)) in the naive assignment and compare the results with the ones obtained in the mirror assignment. We find that, within the naive assignment, we are not able to reproduce the experimental value of the isospin-odd scattering length, while the mirror assignment is in good agreement with it for both choices N (1535) and N (1650). The isospin-even scattering length is not yet conclusive in either assignment because it depends crucially on the poorly known scalar mesonic sector. The decay with Γ N(1535)→Nη turns out to be far too small in both the naive and mirror assignments, while Γ N(1650)→Nη is described correctly by both of them. In conclusions, the mirror assignment with N (1650) as the chiral partner of the nucleon is the favored configuration.

We calculate the pion-nucleon scattering lengths a (±) 0 and the mass parameter m 0 , which describes the nucleon mass in the chiral limit, at tree-level in the framework of a globally symmetric linear sigma model with parity-doubled nucleons. When recent lattice results [1] are used, we obtain * Speaker.