We study the two dimensional vector meson model introduced by Thirring and Wess, that is to say the Schwinger model with massive photon and massless fermion. We prove, with a renormalization group approach, that the vector and axial Ward identities are broken by the Adler–Bell–Jackiw anomaly; and we rigorously establish three widely believed consequences: (a) the interacting meson-meson correlation equals a free boson propagator, although the mass is additively renormalized by the anomaly; (b) the anomaly is quadratic in the charge, in agreement with the Adler–Bardeen formula; (c) the fermion-fermion correlation has an anomalous long-distance decay.