Simultaneous measurement of ${\mathit{K}}_{\mathit{S}}$ and ${\mathit{K}}_{\mathit{L}}$ decays into ${\mathrm{\pi }}^{+}$${\mathrm{\pi }}^{\mathrm{-}}$γ

With the E731 apparatus at Fermilab, we have simultaneously collected 6859 ${\mathit{K}}_{\mathit{L}}$ and ${\mathit{K}}_{\mathit{S}}$ decays into ${\mathrm{\pi }}^{+}$ ${\mathrm{\pi }}^{\mathrm{-}}$γ. Using our sample of over 370 000 ${\mathrm{\pi }}^{+}$ ${\mathrm{\pi }}^{\mathrm{-}}$ decays for normalization we have determined that the ratio Γ(${\mathit{K}}^0$→${\mathrm{\pi }}^{+}$ ${\mathrm{\pi }}^{\mathrm{-}}$γ)/Γ(${\mathit{K}}^0$→${\mathrm{\pi }}^{+}$ ${\mathrm{\pi }}^{\mathrm{-}}$) is (23.0±0.7)×${10}^{\mathrm{-}3}$ for ${\mathit{K}}_{\mathit{L}}$ and (7.10±0.22)×${10}^{\mathrm{-}3}$ for ${\mathit{K}}_{\mathit{S}}$, for photon energies greater than 20 MeV in the kaon center of mass. After removing the inner-bremsstrahlung contribution, we find that the photon energy spectrum of the direct emission decay of the ${\mathit{K}}_{\mathit{L}}$ is consistent with the presence of a vector meson propagator in the form factor.