New measurement of the rare decay $\eta \to {\pi }^0\gamma \gamma$ with the Crystal Ball/TAPS detectors at the Mainz Microtron

A new measurement of the rare, doubly radiative decay $\eta \to {\pi }^0\gamma \gamma$ was conducted with the Crystal Ball and TAPS multiphoton spectrometers together with the photon tagging facility at the Mainz Microtron MAMI. New data on the dependence of the partial decay width, $\Gamma (\eta \to {\pi }^0\gamma \gamma )$, on the two-photon invariant-mass squared, $m^2\left(\gamma \gamma \right)$, as well as a new, more precise value for the decay width, $\Gamma (\eta \to {\pi }^0\gamma \gamma )=(0.33\pm 0.{03}_{\mathrm{tot}})$ eV, are based on analysis of $1.2\times {10}^3\eta \to {\pi }^0\gamma \gamma$ decays from a total of $6\times {10}^7\eta$ mesons produced in the $\gamma p\to \eta p$ reaction. The present results for $d\Gamma (\eta \to {\pi }^0\gamma \gamma )/d{m}^2\left(\gamma \gamma \right)$ are in good agreement with previous measurements and recent theoretical calculations for this dependence.

Figure 1

Two-dimensional density distributions for events selected as the $\gamma p\to {\pi }^0\gamma \gamma p$ candidates obtained from the MC simulations of the three background processes (a) $\gamma p\to {\pi }^0{\pi }^{0}p$, (b) $\gamma p\to \eta p\to \gamma \gamma p$, (c) $\gamma p\to \eta p\to 3{\pi }^{0}p$ and [(d)–(f)] the process under study $\gamma p\to \eta p\to {\pi }^0\gamma \gamma p$. Distributions (a), (d) plot the larger invariant mass $m\left({\pi }^0\gamma \right)$ and (b), (e) plot the smaller $m\left({\pi }^0\gamma \right)$ with respect to $m\left({\pi }^0\gamma \gamma \right)$. Distributions (c), (f) plot the effective radii of the two clusters ascribed to the photons produced not from the ${\pi }^0$ decay. The cuts tested are shown by blue lines. Each of the three cuts on $m_{\max }\left({\pi }^0\gamma \right)$ implies discarding all events that lie above the corresponding line. The cuts on $m_{\min }\left({\pi }^0\gamma \right)$ implies discarding all events that lie below the line. Each of the three cuts on the cluster effective radius discards all events for which at least one of the two $R$ values is above the corresponding line.

Figure 2

$m\left({\pi }^0\gamma \gamma \right)$ invariant-mass distributions obtained for $m^2\left(\gamma \gamma \right)=(0.0375\pm 0.0100)$ ${\mathrm{GeV}}^2/c^4$: (a) MC simulation of the background reaction $\gamma p\to {\pi }^0{\pi }^{0}p$ with a polynomial fit; (b) MC simulation of $\gamma p\to \eta p\to {\pi }^0\gamma \gamma p$ with a Gaussian fit; (c) experimental events from the 2009 data set (crosses) after subtracting the random background; the $\gamma p\to \eta p\to 3{\pi }^{0}p$ background (solid line) expected to remain after all cuts (solid line); (d) experimental events from (c) after subtracting the $\gamma p\to \eta p\to 3{\pi }^{0}p$ background fit with the sum of a Gaussian and a polynomial.

Figure 3

Same as Fig. 2, but for $m^2\left(\gamma \gamma \right)=(0.0775\pm 0.0100)$ ${\mathrm{GeV}}^2/c^4$.

Figure 4

Same as Fig. 2, but for $m^2\left(\gamma \gamma \right)=(0.11875\pm 0.01125)$ ${\mathrm{GeV}}^2/c^4$.

Figure 5

Comparison of the $d\Gamma (\eta \to {\pi }^0\gamma \gamma )/d{m}^2\left(\gamma \gamma \right)$ results obtained from the analyses of the 2007 (red squares) data set with the results from 2009 (blue triangles) and with the calculations of Ref. [22] (short-dashed line), Ref. [4] (solid line with shaded error band), Ref. [5] (dash-dotted line), and Ref. [10] (long-dashed line) fitting to the present data only.

Figure 6

Comparison of the combined $d\Gamma (\eta \to {\pi }^0\gamma \gamma )/d{m}^2\left(\gamma \gamma \right)$ results from the present analysis (black squares) with previous measurements by the CB at AGS [7] (blue triangles) and the A2 at MAMI-B [6] (red circles), and with the calculations of Ref. [22] (short-dashed line), Ref. [4] (solid line with shaded error band), Ref. [5] (dash-dotted line), and Ref. [10] (long-dashed line) fitting to the present data along with the data points of Refs. [6, 7].

Figure 7

Same as Fig. 2, but for the full range of $m^2\left(\gamma \gamma \right)$ from the 2007 data set and using a looser cut on the cluster effective radius, shown by the dashed blue line in Figs. 1 and 1.

Figure 8

Same as Fig. 7, but using a tighter cut on the cluster effective radius, shown by the solid blue line in Figs. 1 and 1.