QCD thermal phase transition in the presence of a small chemical potential

Abstract

We propose a new method to investigate the thermal properties of QCD with a small quark chemical potential $\ensuremath{\mu}.$ Derivatives of quark and gluonic observables with respect to $\ensuremath{\mu}$ are computed at $\ensuremath{\mu}=0$ for two flavors of $p4$ improved staggered fermions with $ma=0.1,0.2$ on a ${16}^{3}\ifmmode\times\else\texttimes\fi{}4$ lattice, and used to calculate the leading order Taylor expansion in $\ensuremath{\mu}$ of the location of the pseudocritical point about $\ensuremath{\mu}=0.$ This expansion should be well behaved for the small values of ${\ensuremath{\mu}}_{\mathrm{q}}{/T}_{c}\ensuremath{\sim}0.1$ relevant for BNL RHIC phenomenology, and predicts a critical curve ${T}_{c}(\ensuremath{\mu})$ in reasonable agreement with estimates obtained using exact reweighting. In addition, we contrast the case of isoscalar and isovector chemical potentials, quantify the effect of $\ensuremath{\mu}\ensuremath{\ne}0$ on the equation of state, and comment on the complex phase of the fermion determinant in QCD with $\ensuremath{\mu}\ensuremath{\ne}0.$