Dilaton-Limit Fixed Point in Hidden Local Symmetric Parity Doublet Model

Abstract: We study nucleon structure with positive and negative parities using a parity doublet model endowed with hidden local symmetry (HLS) with the objective to probe dense baryonic matter. The model -- that we shall refer to as "PDHLS model" for short -- allows a chiral-invariant mass of the nucleons unconnected to spontaneously broken chiral symmetry which comes out to be m_0 ~ 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 non-vanishing at chiral restoration presents a deep issue for the origin of the nucleon mass as well as 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 corresponds exactly to the "dilaton limit" at which the HLS vector mesons decouple from the nucleons before reaching the vector manifestation fixed point. We suggest that cold baryonic system will flow to this limit as density increases toward that of chiral restoration.