Virtual photons in SU(2) chiral perturbation theory and electromagnetic corrections to ππ scattering

We construct the generating functional of two flavor chiral perturbation theory including the effects of virtual photons in the one loop approximation. As an application, we calculate the electromagnetic corrections to the elastic ππ scattering amplitude, in particular to its S-wave threshold parameters. Numerical estimates are given for the reaction π0π0 → π0π0. These electromagnetic effects are found to be smaller than the hadronic two-loop corrections for the scattering length a0. The effective range b0 increases by 36% due to the unitary cusp.