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 ρ ₀ using the constraining bands on the pressure in cold SNM in the density range of 1.3ρ ₀ to 4.5ρ 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 ± 30, −200 ± 200 and −146 ± 1728 MeV, their posterior most probable values are narrowed down to ${192}_{-16}^{+12}$ MeV, −${180}_{-110}^{+100}$ 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 $K_0=220_{-0}^{+6}$ MeV, $J_0=-390_{-70}^{+60}$ 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. (paper)