Examination of $N^*(1535)$ as a probe to observe the partial restoration of chiral symmetry in nuclear matter

We investigate modifications of mass and decay width of $N^*(1535)$ in nuclear matter in a chiral symmetric way. The nucleon and $N^*(1535)$ are introduced by a parity doublet model, and nuclear matter is constructed by one-loop diagrams of the nucleon and $N^*(1535)$. The decay width of $N^*(1535)$ is studied respecting chiral symmetry. Our calculations show that the partial width of $\Gamma_{N^*\to N\pi}$ is slightly broadened by a collisional broadening, and that of $\Gamma_{N^*\to N\eta}$ is drastically suppressed at density. As a result, the total decay width $\Gamma_{\rm tot}$ gets small at density. These modifications, especially the drastic narrowing of partial width of $\Gamma_{N^*\to N\eta}$, together with the dropping of mass of $N^*(1535)$ provide experiments for observing the partial restoration of chiral symmetry in nuclear matter by means of $N^*(1535)$ resonance with useful information.