Reconstruction of baryon number distributions*

Abstract

Abstract The maximum entropy method (MEM) and Gaussian process (GP) regression, which are both well-suited for the treatment of inverse problems, are used to reconstruct net-baryon number distributions based on a finite number of cumulants of the distribution. Baryon number distributions across the chiral phase transition are reconstructed. It is deduced that with the increase of the order of cumulants, distribution in the long tails, i.e., far away from the central number, would become increasingly important. We also reconstruct the distribution function based on the experimentally measured cumulants at the collision energy GeV. Given the sizable error of the fourth-order cumulant measured in the experiments, the calculation of MEM shows that with the increasing fourth-order cumulant, there is another peak in the distribution function developed in the region of the large baryon number. This unnaturalness observed in the reconstructed distribution function could in turn be used to constrain the cumulants measured in the experiments.