Effect of non-uniform efficiency on higher-order cumulants in heavy-ion collisions

We perform a systematic study on the effect of non-uniform track efficiency correction in higher-order cumulant analysis in heavy-ion collisions. Through analytical derivation, we find that the true values of cumulants can be successfully reproduced by the efficiency correction with an average of the realistic detector efficiency for particles with the same charges within each single phase space. During a toy model simulation by tuning the non-uniformity of the efficiency employed in the track-by-track efficiency correction method, the theoretical conclusions are supported and the valid averaged efficiency is found to suppress the statistical uncertainties of the reproduced cumulants dramatically. Thus, the usage of the averaged efficiency requires a careful study for the phase space dependence. This study is important for carrying out precision measurements of higher-order cumulants in heavy-ion collision experiments at present and in future.