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 ${\mathrm{\Theta }}_{\mathrm{QCD}}$. 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 ${\mathrm{\Theta }}_{\mathrm{QCD}}$ ($\omega =0$ or $\pi /2$ and ${\mathrm{\Theta }}_{\mathrm{QCD}}=0$ or $\pi$) are there second-order transitions.

• Received 7 August 2015

DOI:https://doi.org/10.1103/PhysRevD.92.094514