Parity doublet model for baryon octets: ground states saturated by good diquarks and the role of bad diquarks for excited states

Abstract: 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 have been considered up to a few times nuclear saturation density, but in such dense region it is also necessary to consider hyperons. With the chiral invariant masses baryons can stay massive in extreme environments (e.g., neutron stars) where the chiral symmetry restoration takes place. In this work, we generalize the previous $\mbox{SU(2)}_L \times \mbox{SU(2)}_R$ parity models of nucleons to $\mbox{SU(3)}_L \times \mbox{SU(3)}_R$ models of the baryon octet, 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 $(3_L, \bar{3}_R) + (\bar{3}_L, 3_R)$, $(3_L, 6_R) + (6_L, 3_R)$ 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 $(3_L, \bar{3}_R) + (\bar{3}_L, 3_R)$ and $(1_L, 8_R) + (8_L, 1_R)$ representations, while the excited states require $(3_L, 6_R) + (6_L, 3_R)$ representations. Important applications of our model are the chiral restoration for strange quarks at large density and the continuity of diquarks from hadronic to quark matter. We also address the problem of large Yukawa couplings which are enhanced in three-flavor construction.