Effect of limited statistics on higher order cumulants measurement in heavy-ion collision experiments

We have studied the effect of limited statistics of data on the measurement of the different order of cumulants of net-proton distribution assuming that the proton and antiproton follow Poissonian and Binomial distributions. The initial parameters for the distributions are determined from experimental results for the two top center of mass energies ( sNN=200 and 62.4 GeV) in the most central ( 0−5% ) Au+Au collisions at Relativistic Heavy Ion Collider (RHIC). In this simulation, the minimum event statistics needed for accurate determination of fourth ( C4 ) and sixth ( C6 ) order cumulants if the signal strength (phase transition or critical point) is at a level of 5% (10%) above the statistical level, is of the order 10 6 (10 5.6 ) and 10 9 (10 8.6 ), respectively. We also present a study on the determination of the statistical error on cumulants using delta theorem, bootstrap and sub-group methods. We have verified their suitability by employing a Monte Carlo procedure. Based on our study we find that the bootstrap method provides a robust way for statistical error estimation on higher order cumulants. These studies will help the experiments to arrive at the minimum required event statistics and the choice of proper method for statistical error estimation for higher order cumulant measurements.