Probing QCD Phase Structure by Baryon Multiplicity Distribution

Abstract

The canonical partition functions $Z_n$ and the number distributions $P_n$ which are obervable in experiments, are related by a single parameter, the fugacities $\xi =\exp (\mu /T)$. With the charge parity invariance, $Z_n$ and $\xi$ can be determined. Thermodynamic quantities such as the number density susceptibility and the kurtosis are then calculated from the grand canonical partition function $Z(\xi ,T)=\sum Z_n(T){\xi }^n$, ($n=-N_{\max },\cdots ,N_{\max }$), for any chemical potential $\mu$, although the region over which the results are reliable for these quantities is constrained by $N_{\max }$. We then calculate the Lee-Yang zeros, which are the zeros of $Z(\xi )$ in the complex fugacity plane, as poles of $d\log Z(\xi )/d\xi$ by using the Cauchy integral theorem. With the help of a multiple precision library, this method provides any precision required without misidentification of the zeros. We analyse $Z_n$ from the net-proton number distributions recently measured at the Relativistic Heavy Ion Collider (RHIC) by assuming the net-proton number is approximately propotional to that of the baryon after the freeze-out, and calculate the moments. We also evaluate the Lee-Yang zero structures obtained from RHIC data and compare them with those obtained from lattice quantum chromodynamics (QCD) calculations. Possible regions of QCD phase transition lines are estimated from the thermodynamics quantities and the Lee-Yang zeros. We discuss how the limited $N_{\max }$ in both experimental and numerical studies affects the reliability of the thermodynamic results and Lee-Yang zeros.

References in corpus (10)

• The renormalization group and quark number fluctuations in the Polyakov loop extended quark-meson model at finite baryon density
• QCD Critical Point and Complex Chemical Potential Singularities
• Imaginary Chemical Potential Approach for the Pseudo-Critical Line in the QCD Phase Diagram with Clover-Improved Wilson Fermions
• How to get from imaginary to real chemical potential
• QCD at Zero Baryon Density and the Polyakov Loop Paradox
• Wilson Fermion Determinant in Lattice QCD
• Lee-Yang zero distribution of high temperature QCD and Roberge-Weiss phase transition
• Search for the QCD Critical Point by Higher Moments of Net-proton Multiplicity Distributions at STAR
• Mapping the phase diagram of strongly interacting matter
• Stable Yang-Lee zeros in truncated fugacity series from net-baryon number multiplicity distribution

Cited by in corpus (13)

• Finite-density lattice QCD and sign problem: current status and open problems
• Lee-Yang zeros in lattice QCD for searching phase transition points
• Topological feature and phase structure of QCD at complex chemical potential
• Canonical approach to finite density QCD with multiple precision computation
• Fourier coefficients of the net-baryon number density and chiral criticality
• Path optimization for $U(1)$ gauge theory with complexified parameters
• From Hagedorn to Lee-Yang: Partition functions of $\mathcal{N}=4$ SYM theory at finite $N$
• Stable Yang-Lee zeros in truncated fugacity series from net-baryon number multiplicity distribution
• Multiplicity, probabilities, and canonical sectors for the cold QCD matter
• Information theoretical view of QCD effective model with heavy quarks
• Condensation of Lee-Yang zeros in scalar field theory
• Taylor expansion and the Cauchy Residue Theorem for finite-density QCD
• Singularities around the QCD critical point in the complex chemical potential plane