Cumulants and central moments of net-charge, net-baryon and net-strangeness distributions in \(^{197}\)Au \(+\) \(^{197}\)Au collisions at \(E_{\textrm{lab}}\) \(=10A\), 20A, 30A and 40A GeV using the UrQMD model

We study the first four cumulants and central moments of the distributions of net-charge, net-baryon number and net-strangeness by using \(^{197}\)Au+\(^{197}\)Au collision events generated by the ultra-relativistic quantum molecular dynamics (UrQMD) model at incident beam energies \(E_{\textrm{lab}}\) \(=10A\), 20A, 30A and 40A GeV in the fixed target configuration. We study the dependence on the collision centrality of these cumulants and moments, and dependence on the pseudorapidity interval size of the central moments in different transverse momentum acceptances. Simulation results are compared with the Skellam distribution (SD) and negative binomial distribution (NBD). In most of the cases, the central moments are found to scale with the number of participating nucleons following the prediction of the central limit theorem. The effects of high baryon density and global conservation principle are quite visible in our results. Not many experimental results on the cumulants and central moments of distributions of conserved quantities are available in the energy domain considered in our analysis. This simulation study will therefore act as a reference baseline prediction for heavy-ion collision experiments at the FAIR and NICA energies.