Probing QCD phase structure using baryon multiplicity distribution

We propose a new method to construct canonical partition functions of quantum chromodynamics (QCD) from net number distributions, such as net baryon, net charge, and net strangeness, by using only the CP symmetry. To demonstrate the method, we apply it to the net-proton number distribution P-n recently measured at the Relativistic Heavy Ion Collider. We show that both mu/T and the canonical partition functions Z(n) are determined by using the CP invariance Z(n) = Z(-n). Comparing mu/T obtained from the present analysis for the net-proton distribution and that obtained from a thermal statistical model, we find remarkable agreement for a wide range of beam energies. Constructing a grand canonical partition function Z(mu, T) = Sigma(n) Z(n)(T)xi(n), we study moments and Lee-Yang zeros for RHIC data, and discuss the possible regions of a phasetransition line in QCD. This is the first Lee-Yang zero diagram obtained for RHIC data, which helps us to see contributions of large net-proton data for exploring the QCD phase diagram. We also calculate Z(n) by the lattice QCD simulations, and find a clear indication of a RobergeWeiss phase transition in the quark-gluon plasma phase. The method does not rely on Taylor expansions, which prevent us going to large mu/T.