Electromagnetic corrections in the anomaly sector

Abstract

Chiral perturbation theory in the anomaly sector for $N_f=2$ is extended to include dynamical photons, thereby allowing a complete treatment of isospin breaking. A minimal set of independent chiral lagrangian terms is determined and the divergence structure is worked out. There are contributions from irreducible and also from reducible one-loop graphs, a feature of ChPT at order larger than four. The generating functional is non-anomalous at order $e^2{p}^4$, but not necessarily at higher order in $e^2$. Practical applications to $\gamma \pi \to \pi \pi$ and to the ${\pi }^0\to 2\gamma$ amplitudes are considered. In the latter case, a complete discussion of the corrections beyond current algebra is presented including quark mass as well as electromagnetic effects.

Comments: 26 pages, 3 figures