We present a straightforward generalization of the results of some previous treatments, in which the Adler-Bell-Jackiw anomaly has been recovered with the help of dispersion relations. We consider the absorptive part of the $\mathrm{VVA}$ triangle diagram with the external momenta $k$, $p$ at vector vertices such that $k^2=p^2<~0$ and the fermion mass $m>~0$. An integral of the imaginary part of the relevant invariant amplitude is calculated explicitly and shown to produce the desired anomalous contribution to the axial Ward identity. This also enables one to demonstrate the $\delta$-like behavior of such an imaginary part in the limit $k^2\to 0$, $m\to 0$.

• Received 5 February 1985

DOI:https://doi.org/10.1103/PhysRevD.32.1029