Vacuum phenomenology of the chiral partner of the nucleon in a linear sigma model with vector mesons

Susanna Gallas; Francesco Giacosa; Dirk H. Rischke

doi:10.1103/PhysRevD.82.014004

paper

Vacuum phenomenology of the chiral partner of the nucleon in a linear sigma model with vector mesons

arXiv:0907.5084 · doi:10.1103/PhysRevD.82.014004

Abstract

We investigate a linear sigma model with global chiral $U (2)_{R} \times U (2)_{L}$ 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, $N^{*}$ , which is usually identified with N(1535). 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, $g_{A}^{N}$ , and its partner, $g_{A}^{N^{*}}$ . Using experimental data for the decays $N^{*} \to N π$ and $a_{1} \to π γ$ , as well as lattice results for $g_{A}^{N^{*}}$ we infer $m_{0} \sim 500$ 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 $N^{*} \to N η$ and the s-wave nucleon-pion scattering lengths $a_{0}^{(\pm)}$ .

16 pages, 2 figures. To appear in Phys. Rev. D

Vacuum phenomenology of the chiral partner of the nucleon in a linear sigma model with vector mesons

Abstract

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