On $Z \to \gamma \gamma$ decay and cancellation of axial anomaly in $Z \to \gamma \gamma$ transition amplitude for massive fermions

Abstract

$Z \to \gamma \gamma$ decay amplitude is considered and proven to be zero due to properties of polarization vectors and Bose statistics. Triangular diagrams for a pseudoscalar $\to \gamma \gamma$ and $Z \to \gamma \gamma$ processes with massive fermions in the loop are explicitely calculated. In the Standard Model axial anomaly vanishes in the sum of these diagrams as Z boson is mixed with one of the Goldstone bosons.