Catalysis of partial chiral symmetry restoration by Delta matter

Abstract: We study the phase structure of dense hadronic matter including $\Delta(1232)$ as well as N(939) 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, $\Delta$ enters into matter in the density region of about one to four times of normal nuclear matter density, $\rho_B \sim 1 - 4\rho_0$. The onset density of $\Delta$ matter depends on the chiral invariant mass of $\Delta$, $m_{\Delta0}$: The lager $m_{\Delta0}$, the bigger the onset density. The $\Delta$ matter of $\rho_B \sim 1 - 4\rho_0$ is unstable due to the existence of $\Delta$, and the stable $\Delta$-nucleon matter is realized at about $\rho_B \sim 4\rho_0$, i.e., the phase transition from nuclear matter to $\Delta$-nucleon matter is of first order for small $m_{\Delta0}$, and it is of second order for large $m_{\Delta0}$. We find that, associated with the phase transition, the chiral condensate changes very rapidly, i.e., the chiral symmetry restoration is accelerated by \Delta matter. As a result of the accelerations, there appear $N^*$(1535) and $\Delta$(1700), which are the chiral partners to N(939) and ${\Delta}$(1232), in high density matter, signaling the partial chiral symmetry restoration. Furthermore, we find that complete chiral symmetry restoration itself is delayed by $\Delta$ matter. We also calculate the effective masses, pressure and symmetry energy to study how the transition to $\Delta$ matter affects such physical quantities. We observe that the physical quantities change drastically at the transition density.