Probing QCD phase structure using baryon multiplicity distribution

Abstract

We propose a new method to construct canonical partition functions of QCD from net number distributions such as the 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 Pn recently measured at RHIC. We show that both µ/T and the canonical partition functions Zn are determined by using the CP invariance Zn = Z−n.Comparing µ/T obtained from the present analysis for the net-proton distribution and that obtained from a thermal statistical model, we find remarkable agreement for wide range of beam energies. Constructing a grand canonical partition function Z(µ, T ) = n Zn(T )ξ n , we study moments and Lee-Yang zeros for RHIC data, and discuss possible regions of a phase transition 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 Zn by the lattice QCD simulations, and find a clear indication of Roberge-Weiss phase transition in the QGP phase. The method does not rely on the Taylor expansions, which prevent us to go to large µ/T .

Lee-Yang zeros in lattice QCD for searching phase transition points

“…[27], a new algorithm was proposed to overcome the difficulty: the cut Baum-Kuchen (cBK) 1 1 Figure 1: Schematic diagram to show paths in the cut Baum-Kuchen algorithm, taken from Ref. [27]. We perform the Cauchy's integration, Eq.…”

“…As shown in Ref. [27], the distributions of LYZs can be calculated from the experimental data of the net-proton multiplicity distribution at RHIC [28,29]. Therefore, studies of LYZs of lattice QCD will be useful to compare with ones from data of future experiments.…”

Search of QCD phase transition points in the canonical approach of the NJL model

“…A new method to overcome the difficulty was proposed in Ref. [27]: the cut Baum-Kuchen (cBK) algorithm with multiple-precision arithmetic. In order to solve the equation, we implement the cBK algorithm and a multiple-precision arithmetic package, FMLIB [28].…”

“…Following Refs. [18,27], we choose N max so that the value of N max /V is approximately unchanged when V changes. Figure 2 indicates that the right edges of LYZs, which is defined by a position of min[Im(ξ)] in the first quadrant in the complex ξ plane, approach the expected CP as V increases.…”

Fisher's zeros for SU(3) with Nf flavors and RG flows

“…It was later observed by Fisher [5] that the pattern of the partition function zeros in the complex temperature plane also gives information about the nature of the phase transition. We usually call the partition function zeros in the complex z = e 2β h plane Lee-Yang zeros [6,7,8] and those in the complex temperature plane Fisher zeros. Interestingly, one can perform finite-size scaling analysis on the zeros and extract critical exponents from them [9,10,11].…”