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$η$ mesons in hot and dense asymmetric nuclear matter

We study the $ηN$ 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 $η$-meson have been calculated in the chiral SU(3) model, considering the effect of explicit symmetry breaking term and range terms in the $ηN$ 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 $ηN$ 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 $ηN$ scattering length $a^{ηN}$ on the $η$ meson mass $m^*_η$ and observed that the $m^*_η$ decrease more for increasing the value of scattering length.