Electromagnetic corrections toK→ππ.II. Dispersive matching

We express the leading electromagnetic corrections in $\overrightarrow{K}\pi \pi$ as integrals over the virtual photon squared momentum $Q^2.$ The high $Q^2$ behavior is obtained via the operator product expansion. The low $Q^2$ behavior is calculated using chiral perturbation theory. We model the intermediate $Q^2$ region using resonance contributions in order to enforce the matching of these two regimes. Our results confirm our previous estimates that the electromagnetic corrections provide a reasonably small shift in the $\Delta I=3/2\mathrm{}$ amplitude.