Narrow Results

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 conclusion, the mirror assignment with N(1650) as the chiral partner of the nucleon is the favored configuration.

The dependence of the nucleon mass on the pion mass is studied in the framework of the extended quark sigma model. We apply the modified quark sigma model to analyze the pion–nucleon sigma term. Analytic expressions are derived using the Feynman–Hellman theorem. The field equations are solved in the mean-field approximation. The results are compared with the CP-PACS group and the cloudy bag model. The results indicate that the extended linear sigma model provides good agreement compared to other models in the mean-field approximation.

We explore the hadron properties in dense baryonic matter in a unified way by using a Skyrme model constructed with an effective Lagrangian which includes the ρ and ω vector mesons as hidden gauge bosons and is valid up to O(p⁴) in chiral expansion including the homogeneous Wess-Zumino terms. With the two input values of pion decay constant and the lowest lying vector meson mass which can be fixed in free space, all the other low energy constants in the effective Lagrangian are determined by their master formulas derived from holographic QCD models, which allows us to study the baryonic matter properties with no additional free parameters and thus without ambiguities. We find that the ω field that figures in the homogeneous Wess-Zumino term plays a crucial role in the skyrmion structure and its matter properties. The most striking and intriguing observation is that the pion decay constant that smoothly drops with increasing density in the Skyrmion phase stops decreasing at n_1/2 at which the skyrmions in medium fractionize into half-skyrmions and remains nearly constant in the half-skyrmion phase. In accordance with the large N_c consideration, the baryon mass also stays non-scaling in the half-skyrmion phase. This feature is supported by the nuclear effective field theory with the parameters of the Lagrangian scaling modified at the skyrmion–half-skyrmion phase transition. Our exploration also uncovers the crucial role of the ω meson in multi-baryon systems as well as in the structure of a single skyrmion.