Fourier coefficients of the net-baryon number density

TL;DR

This paper computes Fourier coefficients of the net-baryon number density at imaginary chemical potential using lattice QCD data, revealing insights into phase transitions and singularity structures in QCD.

Contribution

It introduces a novel Filon-type quadrature for calculating Fourier coefficients from lattice data and analyzes their asymptotic behavior related to phase transitions in QCD.

Findings

Sensitivity to chiral scaling below the Roberge-Weiss temperature

Reasonable estimates for the Lee-Yang edge singularity position

Effective analysis across different lattice spacings and quark masses

Abstract

We calculate Fourier coefficients of the net-baryon number as a function of a purely imaginary chemical potential. The asymptotic behavior of these coefficients is governed by the singularity structure of the QCD partition function and thus encodes information on phase transitions. For the calculation of the Fourier coefficients from lattice data of the Bielefeld-Parma collaboration we use a novel Filon-type quadrature, designed for highly oscillatory integrals. We find sensitivity to chiral scaling in a narrow temperature interval below the Roberge-Weiss transition temperature. Scaling fits yield reasonable values for the position of the Lee-Yang edge singularity in the complex chemical potential plane. Our lattice data has been obtained from simulations with (2+1)-flavors of highly improved staggered quarks (HISQ) at imaginary chemical potential on $N_\tau=4, 6$ and $8$ lattices at physical quark masses.