  We present results on the QCD phase diagram for mu_B <= pi T. Our simulations
are performed with an imaginary chemical potential mu_I for which the fermion
determinant is positive. On an 8^3 x 4 lattice with 2 flavors of staggered
quarks, we map out the phase diagram and identify the pseudo-critical
temperature T_c(mu_I). For mu_I/T <= pi/3, this is an analytic function, whose
Taylor expansion is found to converge rapidly, with truncation errors far
smaller than statistical ones. The truncated series may then be continued to
real mu, yielding the corresponding phase diagram for mu_B <~ 500 MeV. This
approach provides control over systematics and avoids reweighting. We compare
it with other recent work.
