A Measurement of the Branching Ratio of $π^0$ Dalitz Decay using $K_L \rightarrow π^0π^0π^0$ Decays
We present a measurement of $B(π^0 \rightarrow e^+e^- γ)/B(π^0 \rightarrow γγ)$, 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 $K_L \rightarrow π^0π^0π^0 \rightarrow γγ~γγ~e^+e^-γ$ decays. We normalize to $K_L \rightarrow π^0π^0π^0 \rightarrow 6γ$ decays. We find $B(π^0 \rightarrow e^+e^- γ)/B(π^0 \rightarrow γγ)$ $(m_{e^+e^-}$ > 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 $B(π^0 \rightarrow e^+e^- γ)/B(π^0 \rightarrow γγ) = [1.1559 \pm 0.0047(stat) \pm 0.0106 (syst)]$%. This result is consistent with previous measurements and the uncertainty is a factor of three smaller than any previous measurement.