Determination of the Parity of the Neutral Pion via Its Four-Electron Decay

We present a new determination of the parity of the neutral pion via the double Dalitz decay ${\pi }^0\to e^{+}{e}^{-}{e}^{+}{e}^{-}$. Our sample, which consists of 30 511 candidate decays, was collected from $K_L\to {\pi }^0{\pi }^0{\pi }^0$ decays in flight at the KTeV-E799 experiment at Fermi National Accelerator Laboratory. We confirm the negative ${\pi }^0$ parity and place a limit on scalar contributions to the ${\pi }^0\to e^{+}{e}^{-}{e}^{+}{e}^{-}$ decay amplitude of less than 3.3% assuming $CPT$ conservation. The ${\pi }^0{\gamma }^{*}{\gamma }^{*}$ form factor is well described by a momentum-dependent model with a slope parameter fit to the final state phase-space distribution. Additionally, we have measured the branching ratio of this mode to be $B({\pi }^0\to e^{+}{e}^{-}{e}^{+}{e}^{-})=(3.26\pm 0.18)\times {10}^{-5}$.

Figure 1

Lowest order Feynman diagram for ${\pi }^0\to e^{+}{e}^{-}{e}^{+}{e}^{-}$. The direct contribution is shown; a second diagram exists with $e_1^{+}$ and $e_2^{+}$ exchanged.

Figure 2

Invariant $e^{+}{e}^{-}{e}^{+}{e}^{-}$ mass for data events identified by the preferred pairing as $K_L\to {\pi }^0{\pi }^0{\pi }_{DD}^0$ (upper panel) and $K_L\to {\pi }^0{\pi }_D^0{\pi }_D^0$ (lower panel).

Figure 3

Distribution of the kinematic variables $x_1$ and $x_2$ for signal event candidates (points) and signal Monte Carlo simulation with best fit form factor parameters (histogram).

Figure 4

Distribution of the angle $\varphi$, in units of $\pi$, between the planes of the two $e^{+}{e}^{-}$ pairs. The histogram shows the Monte Carlo expectation for negative parity.