We study the phase structure of dense hadronic matter including $\mathrm{\Delta }\left(1232\right)$ as well as $N\left(939\right)$ based on the parity partner structure, where the baryons have their chiral partners with a certain amount of chiral invariant masses. We show that, in symmetric matter, $\mathrm{\Delta }$ enters into matter in the density region of about one to four times normal nuclear matter density, ${\rho }_B\sim 1-4{\rho }_0$. The onset density of $\mathrm{\Delta }$ matter depends on the chiral invariant mass of $\mathrm{\Delta },m_{\mathrm{\Delta }0}$: As $m_{\mathrm{\Delta }0}$ increases, the onset density becomes bigger. The stable $\mathrm{\Delta }$-nucleon matter is realized for ${\rho }_B\gtrsim 1.5{\rho }_0$, i.e., the phase transition from nuclear matter to $\mathrm{\Delta }$-nucleon matter is of first order for small $m_{\mathrm{\Delta }0}$, and it is of second order for large $m_{\mathrm{\Delta }0}$. We find that, associated with the phase transition, the chiral condensate changes very rapidly; i.e., the chiral symmetry restoration is accelerated by $\mathrm{\Delta }$ matter. As a result of the accelerations, there appear $N^{*}\left(1535\right)$ and $\mathrm{\Delta }\left(1700\right)$, which are the chiral partners to $N\left(939\right)$ and $\mathrm{\Delta }\left(1232\right)$, in high-density matter, signaling the partial chiral symmetry restoration. Furthermore, we find that complete chiral symmetry restoration itself is delayed by $\mathrm{\Delta }$ matter. We also calculate the effective masses, pressure, and symmetry energy to study how the transition to $\mathrm{\Delta }$ matter affects such physical quantities. We observe that the physical quantities change drastically at the transition density.

• Received 23 April 2017
• Revised 20 July 2017

DOI:https://doi.org/10.1103/PhysRevC.97.065202