Calculation of the second-order weak amplitude for K2 → π0e+e-

The second-order weak amplitude for K₂→π⁰e⁺e⁻ has a finite imaginary part arising from the presence of a πν intermediate state in the channels K₂+e±→π⁰+e±, which we calculate in terms of the amplitudes for $K_2\to {\pi }^{\pm }{e}^{\mp }\nu$ and π±→π⁰e±ν. The real part is determined by means of a dispersion relation, and the result converges for a simple choice of the K₂ₑ₃ and πₑ₃ form factors.