$\eta$ mesons in hot and dense asymmetric nuclear matter

We study the $\eta N$ interactions in the hot and dense isospin asymmetric nuclear matter using two different approaches. In the first approach, the in-medium mass and optical potential of $\eta$ meson have been calculated in the chiral SU(3) model, considering the effect of explicit symmetry-breaking term and range terms in the $\eta N$ interaction Lagrangian density. In the second scenario, the conjunction of chiral perturbation theory and chiral SU(3) model is employed. In this case, the next to leading order $\eta N$ interactions are evaluated from the chiral perturbation theory (ChPT), and the in-medium contribution of scalar densities are taken as input from chiral SU(3) model. We observe a larger negative mass shift in the ChPT $+$ chiral model approach compared to the chiral SU(3) model alone as a function of nuclear density. Moreover, the increase in the asymmetry and temperature cause a decrease in the magnitude of mass shift. We have also studied the impact of $\eta N$ scattering length $a^{\eta N}$ on the $\eta$-meson mass $m_{\eta }^{*}$ and observed that the $m_{\eta }^{*}$ decrease mores for increasing values of scattering length.

Figure 1

The in-medium scalar density of nucleons.

Figure 2

In-medium $\eta$-meson mass in the chiral model.

Figure 3

Comparison of the different terms of $\eta$-meson effective mass in chiral model at $a^{\eta N}=1.14$ fm.

Figure 4

The in-medium $\eta$-meson mass as a function of scattering length.

Figure 5

The in-medium $\eta$ meson optical potential in chiral model at $a^{\eta N}=0.91$ fm.

Figure 6

The in-medium $\eta$-meson optical potential in chiral model at $a^{\eta N}=1.02$ fm.

Figure 7

The in-medium $\eta$ meson optical potential in chiral model at $a^{\eta N}=1.14$ fm.

Figure 8

Comparison of in-medium $\eta$-meson mass calculated from chiral model and ChPT.

Figure 9

Comparison of different terms of the effective mass of $\eta$ meson calculated using unification of ChPT and chiral model at $a^{\eta N}=1.14$ fm.