Electromagnetic Contributions to the Charge Asymmetry in the Semileptonic Decays of Neutral Kaons

While the measured charge asymmetry in the semileptonic decays of ${K_L}^0$ is clear-cut evidence for $\mathrm{CP}$ violation in these processes, the detailed theoretical interpretation of this result is somewhat complicated by the presence of electromagnetic effects. It is shown, however, that whereas these electromagnetic effects can produce sizable differences in decay distributions for decays into charge-conjugate states, their contribution to the asymmetry parameter ${{\delta }_L}^{\pi }$ is not greater than $\frac{\alpha \Gamma \left({K_{l4\mathrm{}}}^0\right)}{\Gamma \left({K_{l3\mathrm{}}}^0\right)}$.