Universal scaling and the asymptotic behaviour of Fourier coefficients of the baryon-number density in QCD

TL;DR

This paper explores the universal scaling of Yang-Lee singularities in QCD to identify phase transitions using lattice data and Fourier coefficients, providing new methods for locating critical points.

Contribution

It introduces two novel approaches—Padé resummation and Fourier coefficient analysis—for extracting the Yang-Lee singularity from lattice QCD data.

Findings

Determined the Roberge-Weiss transition temperature as 211.1 MeV.

Demonstrated the Fourier coefficient method's effectiveness in locating singularities.

Validated the methods using the Quark Meson model.

Abstract

We discuss the scaling of the Yang-Lee singularity (YLs) and show how the universal scaling can be used to locate phase transitions in QCD. We describe two complementary methods to extract the location of the Yang-Lee singularity from lattice QCD data of the baryon-number density and higher order cumulants of the baryon number, obtained at imaginary chemical potential. The first method (multi-point Pad\'e resummation) is used to determine the Roberge-Weiss phase transition temperature. Our continuum extrapolated result is $T_{RW}=211.1\pm3.1$ MeV. The second method is based on the asymptotic behaviour of the Fourier coefficients of the baryon-number density. We discuss the derivation of a fitting function and demonstrate that the procedure can successfully locate the YLs in the Quark Meson model.