A Measurement of the Branching Ratio of $pi^0$ Dalitz Decay using $K_L ightarrow pi^0pi^0pi^0$ Decays.

We present a measurement of $B(pi^0 rightarrow e^+e^- gamma)/B(pi^0 rightarrow gammagamma)$, the Dalitz branching ratio, using data taken in 1999 by the E832 KTeV experiment at Fermi National Accelerator Laboratory. We use neutral pions from fully reconstructed $K_L$ decays in flight; the measurement is based on about 60 thousand $K_L rightarrow pi^0pi^0pi^0 rightarrow gammagamma~gammagamma~e^+e^-gamma$ decays. We normalize to $K_L rightarrow pi^0pi^0pi^0 rightarrow 6gamma$ decays. We find $B(pi^0 rightarrow e^+e^- gamma)/B(pi^0 rightarrow gammagamma)$ $(m_{e^+e^-}$ u003e 15 MeV/$c^2)$ = $[3.920 pm 0.016(stat) pm 0.036 (syst)] times 10^{-3}$. Using the Mikaelian and Smith prediction for the $e^+e^-$ mass spectrum, we correct the result to the full $e^+e^-$ mass range. The corrected result is $B(pi^0 rightarrow e^+e^- gamma)/B(pi^0 rightarrow gammagamma) = [1.1559 pm 0.0047(stat) pm 0.0106 (syst)]$%. This result is consistent with previous measurements and theoretical predictions. The uncertainty is a factor of three smaller than any previous measurement.