New high-statistics measurement of the $π^0 \to e^+e^-γ$ Dalitz decay at the Mainz Microtron

TL;DR

The paper addresses the time-like electromagnetic transition form factor of the π^0 through the Dalitz decay $\pi^0\to e^+e^-\gamma$, a key input for hadronic light-by-light contributions to the muon anomalous magnetic moment $(g-2)_\mu$. Using the A2 setup at MAMI, the authors analyze $\gamma p\to \pi^0 p\to e^+e^-\gamma p$ with ~3.31×10^9 produced $\pi^0$ mesons, yielding about $2.4\times10^6$ Dalitz decays and extracting the slope parameter $a_\pi=0.0315\pm0.0026_{\mathrm{stat}}\pm0.0010_{\mathrm{syst}}$. They present $|F_{\pi^0\gamma}(m_{ee})|^2$ in 22 bins over $m_{ee}$ from 15 to 125 MeV/$c^2$, and compare to previous measurements and theoretical models (Padé and dispersive analyses), finding overall agreement and improved precision. The results help constrain low-energy QCD and HLbL inputs, though the uncertainties remain too large to significantly refine $(g-2)_\mu$ beyond current data-driven estimates. The work provides a high-statistics benchmark for time-like TFFs and furnishes data for model-independent fits and future analyses.

Abstract

The Dalitz decay $π^0 \to e^+e^-γ$ has been measured with the highest statistical accuracy obtained so far in the $γp\to π^0 p$ reaction with the A2 tagged-photon facility at the Mainz Microtron, MAMI. The value of the slope parameter for the $π^0$ electromagnetic transition form factor, $a_π=0.0315\pm 0.0026_{\mathrm{stat}}\pm 0.0010_{\mathrm{syst}}$, is obtained from the analysis of $2.4\times10^6$ $π^0 \to e^+e^-γ$ observed decays. Within experimental uncertainties, it is in agreement with existing measurements and theoretical calculations, with its own uncertainty being smaller than previous results based on the analysis of $π^0\to e^+e^-γ$ decays.

Figures (9)

• Figure 1: (Color online) Experimental events selected as $\gamma p\to e^+e^-\gamma p$ candidates by requiring the kinematic-fit CL($\gamma p\to 3\gamma p$)$>$1% and $e^{\pm}$ to be identified by using $dE/dx$ from the PID to suppress their misidentification with recoiling protons: (a) the two-dimensional distribution of $m(e^+e^-\gamma)$ vs $m(e^+e^-)$; (b) the $m(e^+e^-\gamma)$ distribution fitted with the sum of a Gaussian for the $\pi^0 \to e^+e^-\gamma$ peak (blue line) and a polynomial of order 4 for the background (green line), and the subtracted empty-target background shown by the magenta line.
• Figure 2: (Color online) $m(e^+e^-\gamma)$ invariant-mass distributions obtained in the range $40<m(e^+e^-)<45$ MeV/$c^2$ with $\gamma p\to e^+e^-\gamma p$ candidates selected without using a $dE/dx$ PID cut to separate $e^{\pm}$ from the recoil protons: (a) MC simulation of $6.2\times10^9$$\gamma p\to \pi^0 p \to \gamma\gamma p$ events; (b) MC simulation of $1.6\times10^8$$\gamma p\to \pi^0 p \to e^+e^-\gamma p$ events; (c) experimental spectrum (solid triangles with error bars) fitted with the sum of the $\gamma p\to \pi^0 p \to e^+e^-\gamma p$ and $\gamma p\to \pi^0 p \to \gamma\gamma p$ MC simulations (shown by the blue line), with the fraction of the $\gamma p\to \pi^0 p \to \gamma\gamma p$ background shown by the red line.
• Figure 3: (Color online) Same as Fig. \ref{['fig:pi0eeg_2018_mee40_45mev_hfit_3x1']}, but with the use of a $dE/dx$ PID cut to separate $e^{\pm}$ from the recoil protons.
• Figure 4: (Color online) Same as Fig. \ref{['fig:pi0eeg_2018_mee40_45mev_hfit_3x1']}, but for the invariant-mass range $100<m(e^+e^-)<105$ MeV/$c^2$.
• Figure 5: (Color online) Same as Fig. \ref{['fig:pi0eeg_2018_mee100_105mev_hfit_3x1']}, but with using a $dE/dx$ PID cut to separate $e^{\pm}$ from the recoil protons.