In-medium pion dispersion relation and medium correction of $N\pi\leftrightarrow \Delta$ near the threshold energy of pion production

Transport models cannot simultaneously explain very recent data on pion multiplicities and pion charged ratios from central collision of Sn+Sn at 0.27 A GeV. This stimulates further investigations on the pion dispersion relation, in-medium \begin{document}$N\pi\to \Delta$\end{document} cross sections, and \begin{document}$\Delta \to N \pi$\end{document} decay widths near the threshold energy or at subthreshold energy of pion production in isospin asymmetric nuclear matter. In this study, the pion dispersion relation, in-medium \begin{document}$N\pi\to \Delta$\end{document} cross section, and \begin{document}$\Delta \to N \pi$\end{document} decay width near the threshold energy are investigated in isospin asymmetric nuclear matter by using the one-boson-exchange model. With the consideration of the energy conservation effect, the in-medium \begin{document}$N\pi\to\Delta$\end{document} cross sections are enhanced at \begin{document}$s^{1/2} GeV in a nuclear medium. The prediction of pion multiplicity and \begin{document}$\pi^-/\pi^+$\end{document} ratios near the threshold energy could be modified if this effect is considered in transport model simulations.