Insights on pion production mechanism and symmetry energy at high density

Abstract

The $N\hat{I}”\to NN$ cross sections, which take into account the $\hat{I}”$-mass dependence of M-matrix and momentum $p_{N\hat{I}”}$, are applied on the calculation of pion production within the framework of the UrQMD model. Our study shows that UrQMD calculations with the $\hat{I}”$-mass dependent $N\hat{I}”\to NN$ cross sections enhance the pion multiplicities and decrease the $\ddot{I}{€}^{-}/\ddot{I}{€}^{+}$ ratios. By analyzing the time evolution of the pion production rate and the density in the overlapped region for Au+Au at the beam energy of 0.4A GeV, we find that the pion multiplicity probes the symmetry energy in the region of 1-2 times normal density. The process of pion production in the reaction is tracked including the loops of $NN\leftrightarrow N\hat{I}”$ and $\hat{I}”\leftrightarrow N\ddot{I}€$, our calculations show that the sensitivity of $\ddot{I}{€}^{-}/\ddot{I}{€}^{+}$ to symmetry energy is weakened after 4-5 N-$\hat{I}”$-$\ddot{I}€$ loops in the pion production path, while the $\ddot{I}{€}^{-}/\ddot{I}{€}^{+}$ ratio in reactions at near threshold energies remains its sensitivity to the symmetry energy. By comparing the calculations to the FOPI data, we obtain a model dependent conclusion on the symmetry energy and the symmetry energy at two times normal density is $S(2\ddot{I}{}_0)$=38-73 MeV within $1\ddot{I}ƒ$ uncertainties. Under the constraints of tidal deformability and maximum mass of neutron star, the symmetry energy at two times normal density is reduced to $48-58$ MeV and slope of symmetry energy $L=54-81$ MeV, and it is consistent with the constraints from ASY-EOS flow data.

11 pages, 9 fiigures