Insights into the pion production mechanism and the symmetry energy at high density

The pion production mechanism is explored based on the ultrarelativistic quantum molecular dynamics model (UrQMD) in which $\mathrm{\ensuremath{\Delta}}$-mass dependence of $\mathcal{M}$ matrix and momentum ${p}_{N\mathrm{\ensuremath{\Delta}}}$ $N\mathrm{\ensuremath{\Delta}}\ensuremath{\rightarrow}NN$ cross sections are taken into account. By analyzing time evolution rate density overlapped region for reaction Au+Au at beam energy $0.4A$ GeV, we find that characteristic observable 1--2 times normal density. process tracked, including loops $NN\ensuremath{\leftrightarrow}N\mathrm{\ensuremath{\Delta}}$ $\mathrm{\ensuremath{\Delta}}\ensuremath{\leftrightarrow}N\ensuremath{\pi}$, our calculations show sensitivity ${\ensuremath{\pi}}^{\ensuremath{-}}/{\ensuremath{\pi}}^{+}$ to symmetry weakened after 4--5 $N\text{\ensuremath{-}}\mathrm{\ensuremath{\Delta}}\text{\ensuremath{-}}\ensuremath{\pi}$ path. ratio near threshold energies retains its energy, it insensitive nuclear incompressibility ${K}_{0}$ effective mass when their values selected commonly accepted range. comparing UrQMD FOPI data GeV considering constraint from neutron star properties, slope $L=54--91$ MeV two $S(2{\ensuremath{\rho}}_{0})=48--59$ deduced, they also consistent with ASY-EOS flow data.