Chiral perturbation theory in a θ vacuum

We consider chiral perturbation theory with a nonzero θ term. Because of the CP violating term, the vacuum of chiral fields is shifted to a nontrivial element on the SU(Nf) group manifold. The CP violation also provides mixing of different CP eigenstates, between scalar and pseudoscalar, or vector and axialvector, operators. We investigate up to O(θ2) effects on the mesonic two-point correlators of chiral perturbation theory to the one-loop order. We also address the effects of fixing topology, by using saddle-point integration in the Fourier transform with respect to θ.