Watsonʹs theorem and electromagnetism in K→ππ decay

We consider what constraints unitarity and CPT invariance yield on the strong and electromagnetic phases entering K→ππ 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 π+π−γ channel. This demonstrates that Watsonʹs theorem can be extended to include the presence of electromagnetism. We point out the consequences for the general structure of the K→ππ decay amplitudes in the presence of isospin violation.