Effects of kinematic cuts on net-electric charge fluctuations

Abstract

The effects of kinematic cuts on electric charge fluctuations in a gas of charged particles are discussed. We consider a very transparent example of an ideal pion gas with quantum statistics, which can be viewed as a multi-component gas of Boltzmann particles with different charges and masses. Cumulants of net-electric charge fluctuations ${\chi }_n^Q$ are calculated in a static and expanding medium with flow parameters adjusted to the experimental data. We show that the transverse momentum cut, $p_{t_{\text{min}}}\le p_t\le p_{t_{\text{max}}}$, weakens the effects of Bose statistics, i.e. contributions of effectively multi-charged states to higher order moments. Consequently, cuts in $p_t$ modify the experimentally measured cumulants and their ratios. We discuss the influence of kinematic cuts on the ratio of mean and variance of electric charge fluctuations in a hadron resonance gas, in the light of recent data of the STAR and PHENIX Collaborations. We find that the different momentum cuts of $p_{t_{\text{min}}}=0.2$~GeV (STAR) and $p_{t_{\text{min}}}=0.3$~GeV (PHENIX) are responsible for more than 30\% of the difference between these two data sets. We argue that the $p_t$ cuts imposed on charged particles will influence the normalized kurtosis {${\kappa }_Q{\sigma }_Q^2={\chi }_4^Q/{\chi }_2^Q$} of the electric charge fluctuations. In particular, the reduction of ${\kappa }_Q{\sigma }_Q^2$ with increasing $p_{t_{\text{min}}}$ will lead to differences between PHENIX and STAR data of $\mathcal{O}(6\%)$ which currently are buried under large statistical and systematic errors. We furthermore introduce the relation between momentum cut-off and finite volume effects, which is of relevance for the comparison between experimental data and lattice QCD calculations.

10 pages, 11figures, Section II is extended. To appear in Phys.Rev.C

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