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

We propose a new method to investigate the thermal properties of QCD with a small quark chemical potential $\mu .$ Derivatives of quark and gluonic observables with respect to $\mu$ are computed at $\mu =0\mathrm{}$ for two flavors of $p4\mathrm{}$ improved staggered fermions with $ma=0.1,0.2\mathrm{}$ on a ${16}^3\times 4$ lattice, and used to calculate the leading order Taylor expansion in $\mu$ of the location of the pseudocritical point about $\mu =0.\mathrm{}$ This expansion should be well behaved for the small values of ${\mu }_{\mathrm{q}}{/T}_c\sim 0.1$ relevant for BNL RHIC phenomenology, and predicts a critical curve $T_c\left(\mu \right)$ 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 $\mu \ne 0$ on the equation of state, and comment on the complex phase of the fermion determinant in QCD with $\mu \ne 0.$