Quantum Discrete Symmetry and the Strong CP Problem

We study a 2N-flavor effective theory of N-flavor QCD. With the axial anomaly accounted for in the effective theory by a 't Hooft interaction, only QCD conserved currents survive. However, there is a residual discrete symmetry with interesting properties. With non-vanishing quark masses, this S_2 symmetry is broken unless \bar\theta=0 or pi. We further show that there is a sense in which hadrons in the effective theory fall into S_2 multiplets. Surprisingly, predictions of this multiplet structure in the four-flavor effective theory are in good agreement with experiment and have been found previously by imposing Regge asymptotic constraints on pion-hadron scattering amplitudes.