# Catalysis of partial chiral symmetry restoration by Delta matter

## TL;DR

This paper investigates how the inclusion of Delta baryons influences the phase structure of dense hadronic matter, revealing accelerated chiral symmetry restoration and phase transitions dependent on the Delta's chiral invariant mass.

## Contribution

It introduces a model incorporating Delta baryons with chiral partners, analyzing their impact on phase transitions and chiral symmetry restoration in dense matter.

## Key findings

- Delta enters matter at 1-4 times nuclear density
- Chiral symmetry restoration is accelerated by Delta matter
- Physical quantities change drastically at transition density

## 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.