# A Measurement of the Branching Ratio of $\pi^0$ Dalitz Decay using $K_L \rightarrow \pi^0\pi^0\pi^0$ Decays

## TL;DR

This paper reports a precise measurement of the Dalitz decay branching ratio of the neutral pion, using data from the KTeV experiment, improving the accuracy over previous results.

## Contribution

The study provides the most precise measurement to date of the $\pi^0$ Dalitz decay branching ratio, utilizing a large dataset and normalization to $K_L$ decays, with corrections based on theoretical mass spectrum predictions.

## Key findings

- Measured branching ratio with a threefold reduction in uncertainty.
- Results consistent with previous measurements.
- Provides a corrected full mass range branching ratio.

## Abstract

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