Pressure and non-linear susceptibilities in QCD at finite chemical potentials

TL;DR

This paper investigates how the calculation of non-linear quark number susceptibilities in lattice QCD depends on the chemical potential prescription and explores methods to remove this dependence through continuum extrapolation.

Contribution

It demonstrates the prescription dependence of non-linear susceptibilities at finite lattice spacing and shows how to eliminate this dependence via continuum extrapolation in quenched QCD.

Findings

Prescription dependence varies with lattice spacing.

Continuum extrapolation removes the prescription dependence.

Pressure dependence on chemical potential is obtained.

Abstract

When the free energy density of QCD is expanded in a series in the chemical potential, mu, the Taylor coefficients are the non-linear quark number susceptibilities. We show that these depend on the prescription for putting chemical potential on the lattice, making all extrapolations in chemical potential prescription dependent at finite lattice spacing. To put bounds on the prescription dependence, we investigate the magnitude of the non-linear susceptibilities over a range of temperature, T, in QCD with two degenerate flavours of light dynamical quarks at lattice spacing 1/4T. The prescription dependence is removed in quenched QCD through a continuum extrapolation, and the dependence of the pressure, P, on mu is obtained.