Measurements of the Decay $K_L \to e^+e^-\gamma$

The E799-II (KTeV) experiment at Fermilab has collected 83262 $K_L \to e^+e^-\gamma$ events above a background of 79 events. We measure a decay width, normalized to the $K_L \to \pi^0\pi^0\pi^0_D$ (\pi^0 \to \gamma\gamma, \pi^0 to \gamma\gamma, \pi^0_D \to e^+e^-\gamma) decay width, of $\Gamma($K_L \to e^+e^-\gamma$)/\Gamma(K_L \to \pi^0\pi^0\pi^0_D) = (1.3302 \pm 0.0046_{stat} \pm 0.0102_{syst}) \times 10^{-3}$. We also measure parameters of two $K_L \gamma^{\ast}\gamma$ form factor models. In the Bergstrom, Masso, and Singer (BMS) parametrization, we find $\caks = -0.517 \pm 0.030_{stat} \pm 0.022_{syst}$. We separately fit for the first parameter of the D'Ambrosio, Isidori, and Portoles (DIP) model and find $\adip = -1.729 \pm 0.043_{stat} \pm 0.028_{syst}$.