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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, $rho_B sim 1 - 4rho_0$. 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 $rho_B sim 1 - 4rho_0$ is unstable due to the existence of $Delta$, and the stable $Delta$-nucleon matter is realized at about $rho_B sim 4rho_0$, 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.
The partial restoration of chiral symmetry in nuclear medium is investigated in a model independent way by exploiting operator relations in QCD. An exact sum rule is derived for the quark condensate valid for all density. This sum rule is simplified
Recent topics on mesons in nuclei are discussed by especially emphasizing the role of the partial restoration of chiral symmetry in the nuclear medium. The spontaneously broken chiral symmetry in vacuum is considered to be incompletely restored in fi
We shed light upon the eta mass in nuclear matter in the context of partial restoration of chiral symmetry, pointing out that the U_{A}(1) anomaly effects causes the eta-eta mass difference necessarily through the chiral symmetry breaking. As a conse
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