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

TL;DR

This study examines the measurement challenges of the sixth to second order cumulant ratio of net-proton multiplicity in heavy-ion collisions, highlighting current limitations and future prospects with increased statistics.

Contribution

It analyzes the impact of statistical fluctuations and correction methods on cumulant ratio measurements and assesses the potential to observe phase transition signals at RHIC BES II.

Findings

Current statistics are insufficient to reliably extract $C_6/C_2$ at lower energies.

No energy dependence of $C_6/C_2$ observed in simulations with current data.

Potential to detect phase transition signals if they are as strong as predicted by models.

Abstract

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.