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

We explore the relation between proton and nucleon number fluctuations in the final state in relativistic heavy ion collisions. It is shown that the correlations between the isospins of nucleons in the final state are almost negligible over a wide range of collision energy. This leads to a factorization of the distribution function of the proton, the neutron, and their antiparticles in the final state with binomial distribution functions. Using the factorization, we derive formulas to determine nucleon number cumulants, which are not direct experimental observables, from proton number fluctuations, which are experimentally observable in event-by-event analyses. With a simple treatment for strange baryons, the nucleon number cumulants are further promoted to the baryon number ones. Experimental determination of the baryon number cumulants makes it possible to compare various theoretical studies directly with experiments. The effects of nonzero isospin density on this formula are addressed quantitatively. It is shown that the effects are well suppressed over a wide energy range.