Measurement of the ratio of the sixth order to the second order cumulant of net-proton multiplicity distributions in relativistic heavy-ion collisions

We investigate the measurement of the sixth order cumulant and its ratio to the second order cumulant ($C_6/C_2$) in relativistic heavy-ion collisions. The influence of statistics and different methods of centrality bin width correction on $C_6/C_2$ of net-proton multiplicity distributions is demonstrated. There is no satisfactory method to extract $C_6/C_2$ with the current statistics recorded at lower energies by STAR at RHIC. With statistics comparable to the expected statistics at the planned future RHIC Beam Energy Scan II (BES II), no energy dependence of $C_6/C_2$ is observed in central collisions using the UrQMD model. We find if the transition signal is as strong as predicted by the PQM model, then it is hopefully observed at the upcoming RHIC BES II.