Repulsive baryonic interactions and lattice QCD observables at imaginary chemical potential

TL;DR

This paper investigates how Fourier coefficients of baryon density at imaginary chemical potential can reveal baryonic interactions, demonstrating that an interacting hadron resonance gas model with repulsive interactions aligns well with lattice QCD data up to certain temperatures.

Contribution

It introduces the use of Fourier coefficients at imaginary chemical potential as a probe for baryonic interactions and validates an interacting HRG model against lattice QCD results.

Findings

Fourier coefficients are sensitive to baryonic interactions.

Interacting HRG model with eigenvolume matches lattice data up to 185 MeV.

Model reproduces lattice susceptibilities differences up to 175 MeV.

Abstract

The first principle lattice QCD methods allow to calculate the thermodynamic observables at finite temperature and imaginary chemical potential. These can be compared to the predictions of various phenomenological models. We argue that Fourier coefficients with respect to imaginary baryochemical potential are sensitive to modeling of baryonic interactions. As a first application of this sensitivity, we consider the hadron resonance gas (HRG) model with repulsive baryonic interactions, which are modeled by means of the excluded volume correction. The Fourier coefficients of the imaginary part of the net-baryon density at imaginary baryochemical potential -- corresponding to the fugacity or virial expansion at real chemical potential -- are calculated within this model, and compared with the $N_t = 12$ lattice data. The lattice QCD behavior of the first four Fourier coefficients up to $T \simeq 185$ MeV is described fairly well by an interacting HRG with a single baryon-baryon eigenvolume interaction parameter $b \simeq 1$ fm$^3$, while the available lattice data on the difference $\chi_2^B - \chi_4^B$ of baryon number susceptibilities is reproduced up to $T \simeq 175$ MeV.