An effective lagrangian with no U(1) problem in CPn−1 models and QCD

We write an effective lagrangian which gives two-point Green's functions satisfying the anomalous Ward identities for the U(1) axial vector current with a singlet particle that has a non-vanishing mass in the chiral limit. We show that the mechanism that has been postulated by Witten and Veneziano for solving the U(1) problem in the framework of the 1/n expansion in QCD is fully active in the two-dimensional CP^n? model where the 1/n expansion can be explicitly performed.