CP violation in $K_L$→${\pi }^0$$e^{+}$$e^{\mathrm{-}}$: Interference of one-photon and two-photon exchange

The decay $K_L$→${\pi }^0$ $e^{+}$ $e^{\mathrm{-}}$ can proceed through a CP-violating amplitude of order $G_F$ ${\alpha }_{\mathrm{em}\mathrm{\epsilon }}$ or a CP-conserving amplitude of order $G_F$ ${\alpha }_{\mathrm{em}{}^2}$. The latter is shown to be significant, and probably the dominant contribution. Interference of the two pieces produces a large asymmetry between the $e^{+}$ and $e^{\mathrm{-}}$ energy spectra. Some comments are made on the e:μ ratio in $K_L$→${\pi }^0$ $l^{+}$ $l^{\mathrm{-}}$. .AE