Correcting Detector Efficiency Effects in Event-by-Event Net-Proton Fluctuations

Measurements of fluctuations of conserved quantities give valuable information on the susceptibilities of the nuclear matter produced in a heavy-ion collision, and could in principle be used to distinguish QGP from hadronic matter. However, measurements of the cumulants of conserved-quantity distributions are affected by the detector efficiency, which must be accounted for in order to ensure accuracy. Following the development of a toy model that simulates detector efficiency effects on net-proton number, various correction methods, including those developed by A. Bzdak and V. Koch, were implemented and tested in a wide range of conditions. We find that the first four cumulants of net-proton-number distribution can be accurately reproduced by the Koch-Bzdak corrections with reasonable input statistics. Various methods of correcting for $p_T$ dependence of detector efficiency are also explored.