Watson's theorem and electromagnetism in K -> pi pi decay

Abstract

We consider what constraints unitarity and CPT invariance yield on the strong and electromagnetic phases entering K -> pi pi decay. In particular, we show that the relative size of the electromagnetically-induced changes in the I=0 and I=2 phase shifts in the two--pion final state do not depend on the explicit coupling to the pi^+ pi^- gamma channel. This demonstrates that Watson's theorem can be extended to include the presence of electromagnetism. We point out the consequences for the general structure of the K -> pi pi decay amplitudes in the presence of isospin violation.