Parity Doublet Model for Baryon Octets Based on the Quark-line Diagram

Parity doublet model is an effective chiral model that includes the chiral variant and invariant masses of baryons. The chiral invariant mass has large impacts on the density dependence of models which can be constrained by neutron star observations. In the previous work, models of two-flavors to few times nuclear saturation density have been considered, but in such dense region it is also necessary to consider hyperons. In this work, we construct SU(3)_L \otimes SU(3)_R invariant parity doublet models within the linear realization of the chiral symmetry. The major problem in constructing such models has been too many candidates for the chiral representations of baryons. Motivated by the concepts of diquarks and the mended symmetry, we choose the (3_L,\, \bar3_R) + (\bar3_L,\, 3_R), (3_L,\, 6_R) + (6_L,\, 3_R) and (1_L,\, 8_R) + (8_L,\, 1_R) representations and use quark diagrams to constrain the possible types of Yukawa interactions. The masses of the baryon octets for positive and negative baryons up to the first excitations are successfully reproduced. As expected from the diquark considerations, the ground state baryons are well dominated by (3_L,\, \bar3_R) + (\bar3_L,\, 3_R) and (1_L,\, 8_R) + (8_L,\, 1_R) representations, while the excited states require (3_L,\, 6_R) + (6_L,\, 3_R) representations. The model should be useful to consider the chiral restoration for strange quarks at large density and the continuity of diquarks from hadronic to quark matter.