Pressure and nonlinear susceptibilities in QCD at finite chemical potentials

Abstract

When the free energy density of QCD is expanded in a Taylor series in the chemical potential $\ensuremath{\mu},$ the coefficients are the nonlinear quark number susceptibilities. We show that these depend on the prescription for putting the chemical potential on the lattice, making all extrapolations in the chemical potential prescription dependent at finite lattice spacing. To put bounds on the prescription dependence, we investigate the magnitude of the nonlinear susceptibilities over a range of temperature, T, in QCD with two degenerate flavors 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 $\ensuremath{\mu}$ is obtained.