Probing QCD Phase Structure by Baryon Multiplicity Distribution

TL;DR

This paper investigates the QCD phase structure using baryon multiplicity distributions, analyzing Lee-Yang zeros and thermodynamic quantities from experimental data and lattice QCD to identify phase transition regions.

Contribution

It introduces a method to determine Lee-Yang zeros from experimental data and lattice QCD, providing insights into the QCD phase transition structure.

Findings

Lee-Yang zeros reveal potential phase transition points.

Thermodynamic quantities are computed from experimental data.

Limited data range affects the reliability of results.

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 $Z(\xi,T)=\sum Z_n(T) \xi^n$, ($n=-N_{\rm max},\cdots, N_{\rm max}$), for any chemical potential $\mu$, although the region over which the results are reliable for these quantities is constrained by $N_{\rm max}$. 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 $N_{\rm max}$ in both experimental and numerical studies affects the reliability of the thermodynamic results and Lee-Yang zeros.