从相对论性重离子碰撞中的经验压力贝叶斯推断核物质的不可压缩性、偏斜度和峰度
Bayesian inference of the incompressibility, skewness and kurtosis of nuclear matter from empirical pressures in relativistic heavy-ion collisions
摘要：
在贝叶斯统计框架内，利用相对论重离子碰撞中K介子产生和核集体流的输运模型分析，在密度为1.3 ~ 4.5 $ρ_0$的冷对称核物质（SNM）中压力的约束带，推导了SNM在饱和密度$ρ_0$下的不可压缩性$K_0$、偏度$J_0$和峰度$Z_0$参数.作为默认选项，假设$K_0$、$J_0$和$Z_0$具有高斯先验概率分布函数（PDF），其均值和方差为$235\pm 30$、$-200\pm 200$和$-146\pm 1728$ MeV，则它们的后验最可能值分别在68\%置信水平下缩小至192 $^{+12}_{-16}$ MeV、-180 $^{+100}_{-110}$ MeV和200 $^{+250}_{-250}$。结果在很大程度上独立于所使用的$J_0$和$Z_0$的先前PDF。然而，如果人们坚信不可压缩性$K_0$在其220-260 MeV的绝对边界内具有均匀的先验PDF，正如人们可以很容易地在文献中找到的那样，则$K_0$、$J_0$和$Z_0$的后验最可能值分别变为$K_0=220^{+6}_{-0}$ MeV、$J_0=-390^{+60}_{-70}$ MeV和$Z_0=600^{+200}_{-200}$ MeV。虽然SNM EOS参数的后验PDF在某种程度上取决于所使用的$K_0$的先验PDF，但使用不同先验PDF的结果在定性上是一致的。与当前值相比，所有三个参数的不确定性均显著降低，尤其是$J_0$和$Z_0$参数。
英文摘要：
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 1.3$ρ_0$ to 4.5$ρ_0$ 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.
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