Measurement of the rare decay ${\pi }^0\to e^{+}{e}^{-}$

The branching ratio of the rare decay ${\pi }^0\to e^{+}{e}^{-}$ has been measured precisely, using the complete data set from the KTeV E799-II experiment at Fermilab. We observe 794 candidate ${\pi }^0\to e^{+}{e}^{-}$ events using $K_L\to 3{\pi }^0$ as a source of tagged ${\pi }^0$s. The expected background is $52.7\pm 11.2$ events, predominantly from high $e^{+}{e}^{-}$ mass ${\pi }^0\to e^{+}{e}^{-}\gamma$ decays. We have measured $\mathrm{B}({\pi }^0\to e^{+}{e}^{-},(m_{e^{+}{e}^{-}}/m_{{\pi }^0}{)}^2>0.95)=(6.44\pm {0.25}_{\mathrm{stat}}\pm {0.22}_{\mathrm{syst}})\times {10}^{-8}$, which is above the unitary bound from ${\pi }^0\to \gamma \gamma$ and within the range of theoretical expectations from the standard model.

Figure 1

The KTeV spectrometer in E799-II configuration.

Figure 2

Dalitz $x_D\equiv (m_{e^{+}{e}^{-}}/m_{{\pi }^0})$ for fully-reconstructed Dalitz decay candidates after normalization mode analysis cuts. Monte Carlo prediction using the world average form factor slope parameter is overlaid.

Figure 3

Positron-electron invariant mass for ${\pi }^0\to e^{+}{e}^{-}$ signal candidates passing all other cuts. The points with error bars are data; the solid histogram is background MC.

Figure 4

Ratio of data to MC distribution of $m_{e^{+}{e}^{-}}$ in the sideband region below the signal peak, where the MC was normalized to the number of fully-reconstructed Dalitz decays. The dotted line indicates the ratio over the entire region.