A study of the elastic $\pi N$ scattering at finite baryon density

We investigate the elastic $\pi N$ scattering for the $I=3/2$ channel dominated by the $\Delta(1232)$ resonance at finite baryon density $\rho_B$ for the symmetric nuclear matter, employing the effective Lagrangian approach at the tree-level Born approximation. The quark-meson coupling (QMC) model and linear-density approximation are employed to describe the medium modifications for the in-medium baryon properties, such as the nucleon and $\Delta$ masses, and $\Delta$ full decay width. We first reproduce the experimental data in vacuum by fitting the model parameters, then analyze various physical observables including total and differential cross sections, proton-spin asymmetry in medium. It turns out that the $\Delta$-resonance contribution becomes diminished with respect to $\rho_B$, due to the weaker $\pi N$-interaction strength in medium. Beyond the $\Delta$-resonance region $\sqrt{s}\gtrsim1.5$ GeV, the cross sections are almost independent of the density. The present results will be useful to understand the role of the $\Delta$ resonance in the neutron-star equation of state (EoS) as well as in relativistic heavy-ion collision experiments.