What are multiplicity distributions telling us about the QCD phase diagram?

Canonical partition functions Z_n are very valuable tools for studying the QCD phase diagram at a finite temperature and density; they can be calculated from both high-energy heavy-ion collision experimental data and lattice QCD calculations. They help us to understand the features of experimental data from a theoretical point of view. We show that if we construct a whole Z_n(T), then we can obtain information on grand partition functions Z(T,μ/T) for any μ, where μ is the chemical potential. This means that if we obtain information at a fixed value of μ and T, we can obtain Z(T,μ/T) at other values of μ/T by extrapolation. In actual experimental measurements and lattice QCD simulations, a truncation on Z_n is inevitably imposed, i.e., we can only obtain data for a limited number of Z_n(|n|≤N_max). We discuss the consequence of this limitation, and show that the present RHIC data suggest that we are near the QCD phase transition at low energies