Search for a Lee-Yang edge singularity in high-statistics Wuppertal-Budapest data

TL;DR

This study uses high-statistics lattice QCD data to locate the Lee-Yang edge singularity, providing insights into the critical endpoint of the QCD phase diagram and testing different modeling approaches.

Contribution

It estimates the Lee-Yang edge singularity position in QCD using lattice data and compares various functional models for the free energy.

Findings

Estimated the closest singularity in the QCD phase diagram.

Compared different models for the free energy's functional form.

Discussed the predictive power of the modeling approach.

Abstract

Near a critical endpoint the Lee-Yang edge singularity approaches the real axis in the complex chemical potential plane. In the vicinity of the critical point the functional form of this approach depends on the universality class. Assuming a three dimensional Ising critical point in the QCD phase diagram the location of the critical endpoint can be extrapolated provided that the position of the Lee-Yang edge singularity is known at multiple temperatures. A popular method to estimate the position of a singularity is to model the free energy as a rational function of the baryon chemical potential $\mu_\text{B}$. The parameters of this model can be constrained by the cumulants of the net baryon density taken at $\mu_\text{B}^2\leq0$ . Using high-statistics simulations on a lattice $16^3\times8$ by the Wuppertal-Budapest Collaboration we estimate the location of the closest singularity in the QCD phase diagram. We also compare various models for the functional form of the free energy and discuss the predictive power of this approach.