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Binomial acceptance corrections for particle number distributions in high-energy reactions

The binomial acceptance correction procedure is studied for particle number distributions detected in high energy reactions in finite regions of the momentum space. We present acceptance correction formulas for scaled variance, skewness, and kurtosis. Our considerations include various specific types of particles - positively or negatively charged, baryons and antibaryons - as well as conserved charges, namely, the net baryon number and electric charge. A simple model with effects of exact charge conservation, namely the Bessel distribution, is studied in some detail where effects of multi-particle correlations are present. The accuracy of the binomial filter is studied with UrQMD model simulations of inelastic proton-proton reactions. Binomial acceptance correction procedure works well when used inside a small region of phase space as well as for certain efficiency corrections, in particular for constructing net proton fluctuation from net baryon ones. Its performance is less accurate when applied to obtain UrQMD fluctuations in a finite rapidity window from fluctuations in the full $4π$ space.