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We explore the relation between proton and nucleon number fluctuations in thefinal state in relativistic heavy ion collisions. It is shown that thecorrelations between the isospins of nucleons in the final state are almostnegligible over a wide range of collision energy. This leads to a factorizationof the distribution function of the proton, neutron, and their antiparticles inthe final state with binomial distribution functions. Using the factorization,we derive formulas to determine nucleon number cumulants, which are not directexperimental observables, from proton number fluctuations, which areexperimentally observable in event-by-event analyses. With a simple treatmentfor strange baryons, the nucleon number cumulants are further promoted to thebaryon number ones. Experimental determination of the baryon number cumulantsmakes it possible to compare various theoretical studies on them directly withexperiments. Effects of nonzero isospin density on this formula are addressedquantitatively. It is shown that the effects are well suppressed over a wideenergy range.

Relation between baryon number fluctuations and experimentally observed proton number fluctuations in relativistic heavy ion collisions