Bayesian inference of the incompressibility, skewness and kurtosis of nuclear matter from empirical pressures in relativistic heavy-ion collisions

Within the Bayesian statistical framework we infer the incompressibility $K_0$, skewness $J_0$ and kurtosis $Z_0$ parameters of symmetric nuclear matter (SNM) at its saturation density $\rho_0$ using the constraining bands on the pressure in cold SNM in the density range of 1.3$\rho_0$ to 4.5$\rho_0$ from transport model analyses of kaon production and nuclear collective flow in relativistic heavy-ion collisions. As the default option assuming the $K_0$, $J_0$ and $Z_0$ have Gaussian prior probability distribution functions (PDFs) with the means and variances of $235\pm 30$, $-200\pm 200$ and $-146\pm 1728$ MeV, their posterior most probable values are narrowed down to 192$^{+12}_{-16}$ MeV, -180$^{+100}_{-110}$ MeV and 200$^{+250}_{-250}$ at 68\% confidence level, respectively. The results are largely independent of the prior PDFs of $J_0$ and $Z_0$ used. However, if one adopts the strong belief that the incompressibility $K_0$ has a uniform prior PDF within its absolute boundary of 220-260 MeV as one can find easily in the literature, the posterior most probable values of $K_0$, $J_0$ and $Z_0$ shift to $K_0=220^{+6}_{-0}$ MeV, $J_0=-390^{+60}_{-70}$ MeV and $Z_0=600^{+200}_{-200}$ MeV, respectively. While the posterior PDFs of the SNM EOS parameters depend somewhat on the prior PDF of $K_0$ used, the results from using different prior PDFs are qualitatively consistent. The uncertainties of all three parameters are significantly reduced especially for the $J_0$ and $Z_0$ parameters compared to their current values.