Phase structure with nonzero ΘQCD and twisted mass fermions

We determine the phase diagram and chiral condensate for lattice QCD with two flavors of twisted-mass fermions in the presence of nondegenerate up and down quarks, discretization errors and a nonzero value of Theta(QCD). Although such a theory has a complex action and cannot, at present, be simulated, the results are needed to understand how to tune to maximal twist in the presence of electromagnetism, a topic discussed in a companion paper. We find that, in general, the only phase structure is a first-order transition of finite length. Pion masses are nonvanishing throughout the phase plane except at the end points of the first-order line. Only for extremal values of the twist angle and Theta(QCD) (omega = 0 or pi/2 and Theta(QCD) = 0 or pi) are there second-order transitions.