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

Abstract

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 MeV, − MeV and 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 MeV, MeV and 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.