Kinetic Mixing and Axial Charges in the Parity-Doublet Model

The standard parity doublet model with its mass-mixing mechanism fails to describe the axial charge $g_A$ of the nucleon. While $g_A = 1$ in the original Gell-Mann--Levy model, which reproduces the Adler-Bell-Jackiw anomaly of QCD, in the presence of a chirally invariant baryon mass the mass mixing leads to $g_A < 1 $ whereas phenomenologically it is about 1.28. We propose to remedy this problem by introducing kinetic-mixing terms corresponding to meson-baryon derivative couplings, similar in spirit to the two-mixing-angle scenario of the $\eta$-$\eta'$ mixing. This extended parity doublet model contains five parameters in the effective baryonic Lagrangian. Three of them can be determined by using the empirical results for the axial charge of the nucleon together with the masses of the nucleon and its parity partner, the $N^*(1535)$ resonance. We discuss various options how to determine the remaining parameters, touching upon the mass of both parity partners if the chiral condensate is put to zero; the mass of the nucleon in the chiral limit; and the values of meson-baryon coupling constants related to the decays of the resonance to pion-nucleon and sigma-nucleon.