Dilaton-limit fixed point in hidden local symmetric parity doublet model

We study nucleon structure with positive and negative parities using a parity-doublet model endowed with hidden local symmetry with the objective to probe dense baryonic matter. The model-that we shall refer to as the "parity-doublet hidden local symmetry model'' for short-allows a chiral-invariant mass of the nucleons unconnected to spontaneously broken chiral symmetry, which comes out to be m(0) similar to 200 MeV at tree level, from fitting to the decay width of the parity doubler, N(1535), to nucleon-pion and nucleon axial coupling g(A) = 1.267. The presence of a substantial m(0) that remains nonvanishing at chiral restoration presents a deep issue for the origin of the nucleon mass and will affect nontrivially the equation of state for dense baryonic matter relevant for compact stars. We construct a chiral perturbation theory at one-loop order and explore the phase structure of the model using renormalization group equations. We find a fixed point that we identify with the "dilaton limit'' at which the hidden local symmetry vector mesons decouple from the nucleons. We suggest that the cold baryonic system will flow to this limit either before or at reaching the vector manifestation fixed point of hidden local symmetry theory as density increases toward that of chiral restoration.