UrQMD Study of the Effects of Centrality Definitions on Higher Moments of Net Protons at RHIC

A study using UrQMD is presented concerning the higher moments of net protons from Au+Au collisions at 7.7, 11.5, 14.6, 19.6, 27, 39, 62.4, and 200 GeV, concentrating on $C_{4}/C_{2} = \kappa\sigma^{2}$. Higher moments of net protons are predicted to be a sensitive probe of the critical point of QCD. At the QCD critical point, particular ratios of the moments of net protons are predicted to differ from the Poisson baseline. Recently STAR has published the higher moments of net protons for Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 7.7, 11.5, 19.6, 27, 39, 62.4, and 200 GeV. UrQMD quantitatively reproduces STAR's measured $C_{4}/C_{2} = \kappa\sigma^{2}$ for net protons for all Au+Au collisions more central than 30\% and at all centralities for $\sqrt{s_{\rm NN}}$ = 7.7 and 11.5 GeV. The effects are investigated of three different centrality definitions on the values of $C_{4}/C_{2} = \kappa\sigma^{2}$ from UrQMD calculations including the impact parameter given by UrQMD. It is shown that using a centrality definition based on multiplicity to calculate the higher moments of net protons gives a biased answer for $C_{4}/C_{2} = \kappa\sigma^{2}$, except in the most central bin (0-5\%).