Measurement of the ${\pi }^0\to e^{+}{e}^{-}\gamma$ Dalitz decay at the Mainz Microtron

The Dalitz decay ${\pi }^0\to e^{+}{e}^{-}\gamma$ has been measured in the $\gamma p\to {\pi }^{0}p$ reaction with the A2 tagged-photon facility at the Mainz Microtron, MAMI. The value obtained for the slope parameter of the ${\pi }^0$ electromagnetic transition form factor, $a_{\pi }=0.030\pm 0.{010}_{\mathrm{tot}}$, is in agreement with existing measurements of this decay and with recent theoretical calculations. The uncertainty obtained in the value of $a_{\pi }$ is lower than in previous results based on the ${\pi }^0\to e^{+}{e}^{-}\gamma$ decay.

Figure 1

A general sketch of the Crystal Ball, TAPS, and particle identification (PID) detectors.

Figure 2

Comparison of the $e^{+/-}dE/dx$ of the PID for experimental ${\pi }^0\to e^{+}{e}^{-}\gamma$ decays and the MC simulation. The two-dimensional density distribution (with logarithmic scale along plot axis $z)$ for the $e^{+/-}dE/dx$ of the PID versus the energy of the corresponding clusters in the CB is shown in (a) for the experimental data of Run I and in (b) for the MC simulation. The $e^{+/-}dE/dx$ distributions for the experimental data (crosses) and the MC simulation (blue solid line) are compared in (c). The $dE/dx$ distribution from the recoil protons for the selected four-cluster events is shown in (c) by a red solid line.

Figure 3

$m\left(e^{+}{e}^{-}\gamma \right)$ invariant-mass distributions obtained in the analysis of Run I for the $m\left(e^{+}{e}^{-}\right)$ range from 15 to $120\mathrm{MeV}/c^2$ with $\gamma p\to e^{+}{e}^{-}\gamma p$ candidates selected with the kinematic-fit $\mathrm{CL}>1\%$, a $dE/dx$ PID cut accepting the entire range with deposits from $e^{+/-}$, and allowing both $e^{+}$ and $e^{-}$ to be identified with the same PID element: (a) MC simulation of $\gamma p\to {\pi }^{0}p\to e^{+}{e}^{-}\gamma p$ (black dots) fitted with the sum of a Gaussian (blue line) for the actual ${\pi }^0\to e^{+}{e}^{-}\gamma$ peak and a polynomial (green line) of order 4 for the background from misidentifying the recoil proton as either $e^{+}$ or $e^{-}$; (b) experimental spectrum (black dots) after subtracting the background remaining from $\gamma p\to {\pi }^{0}p\to \gamma \gamma p$. The ${\pi }^0\to \gamma \gamma$ background, which is shown by a red line, is normalized to the number of subtracted events. The experimental distribution is fitted with the sum of a Gaussian (blue line) for the ${\pi }^0\to e^{+}{e}^{-}\gamma$ peak and a polynomial (green line) of order 4 for the background.

Figure 4

Same as Fig. 3, but for Run II.

Figure 5

Same as Fig. 3, but requiring both $e^{+}$ and $e^{-}$ to be identified by different PID elements.

Figure 6

The ${\pi }^0\to \gamma {\gamma }^{*}\to \gamma e^{+}{e}^{-}$ angular dependence (in the ${\pi }^0$ rest frame) of the virtual photon decaying into a $e^{+}{e}^{-}$ pair, with ${\theta }^{*}$ being the angle between the direction of one of the leptons in the virtual-photon (or the dilepton) rest frame and the direction of the dilepton system (which is opposite to the $\gamma$ direction): (a) experimental events from the ${\pi }^0\to \gamma e^{+}{e}^{-}$ peak; (b) angular acceptance based on the MC simulation; (c) the experimental spectrum corrected for the acceptance and normalized for comparing to the $1+{cos}^2{\theta }^{*}$ dependence (shown by a red dashed line). Because $e^{+}$ and $e^{-}$ cannot be separated in the present experiment, the angles of both leptons were used, resulting in a symmetric shape with respect to $cos{\theta }^{*}=0.$

Figure 7

$|F_{{\pi }^0\gamma }{|}^2$ results (black filled triangles) obtained from Run I (a), Run II (b), and the combined values (c) are fitted with Eq. (2) (shown by blue lines, with $p0$ being the slope parameter $a_{\pi })$ and compared to the calculations with Padé approximants [25] (shown by a short-dashed magenta line with an error band) and to the dispersive analysis (DA) from Ref. [16] (long-dashed red line). The error band for the latter analysis is narrower by a factor of 4, compared to the other shown, and was omitted because of its smallness. The error bars on all data points represent the total uncertainties of the results.