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A comparative analysis of in-medium spectral functions for $N(940)$ and $N^*(1535)$ in real-time thermal field theory

In the real-time thermal field theory, the nucleon self-energy at finite temperature and density is evaluated where an extensive set of pion-baryon ($πB$) loops are considered. On the other side the in-medium self-energy of $N^*(1535)$ for $πN$ and $ηN$ loops is also determined in the same framework. The detail branch cut structures for these different $πB$ loops for nucleon $N(940)$ and $πN$, $ηN$ loops for $N^*(1535)$ are addressed. Using the total self-energy of $N(940)$ and $N^*(1535)$, which contain the contributions of their corresponding loop diagrams, the complete structures of their in-medium spectral functions have been obtained. The Landau and unitary cut contributions provide two separate peak structures in the nucleon spectral function while $N^*(1535)$ has single peak structure in its unitary cuts. At high temperature, the peak structures of both at their individual poles are attenuated while at high density Landau peak structure of nucleon is completely suppressed and its unitary peak structure is tending to be shifted towards the melted peak of $N^*(1535)$. The non-trivial modifications of these chiral partners may indicate some association of chiral symmetry restoration.