Observation of the doubly radiative decay ${\eta }^{\prime }\to \gamma \gamma {\pi }^0$

Based on a sample of 1.31 billion $J/\psi$ events collected with the BESIII detector, we report the study of the doubly radiative decay ${\eta }^{\prime }\to \gamma \gamma {\pi }^0$ for the first time, where the ${\eta }^{\prime }$ meson is produced via the $J/\psi \to \gamma {\eta }^{\prime }$ decay. The branching fraction of ${\eta }^{\prime }\to \gamma \gamma {\pi }^0$ inclusive decay is measured to be $\mathcal{B}({\eta }^{\prime }\to \gamma \gamma {\pi }^0{)}_{\mathrm{Incl}}=(3.20\pm 0.07(\mathrm{stat})\pm 0.23(\mathrm{sys}))\times {10}^{-3}$, while the branching fractions of the dominant process ${\eta }^{\prime }\to \gamma \omega$ and the nonresonant component are determined to be $\mathcal{B}({\eta }^{\prime }\to \gamma \omega )\times \mathcal{B}(\omega \to \gamma {\pi }^0)=(23.7\pm 1.4(\mathrm{stat})\pm 1.8(\mathrm{sys}))\times {10}^{-4}$ and $\mathcal{B}({\eta }^{\prime }\to \gamma \gamma {\pi }^0{)}_{\mathrm{NR}}=(6.16\pm 0.64(\mathrm{stat})\pm 0.67(\mathrm{sys}))\times {10}^{-4}$, respectively. In addition, the $M_{\gamma \gamma }^2$-dependent partial widths of the inclusive decay are also presented.

Figure 1

Distribution of the ${\chi }_{5C}^2$ of the 5C kinematic fit for the inclusive ${\eta }^{\prime }$ decay. Dots with error bars are data; the heavy (black) solid-curve is the sum of signal and expected backgrounds from MC simulations; the light (red) solid-curves is signal components which are normalized to the fitted yields; the (green) dotted-curve is the class I background; and the (pink) dot-dashed-curve is the class II background.

Figure 2

Results of the fit to $M_{\gamma \gamma {\pi }^0}$ for the selected inclusive ${\eta }^{\prime }\to \gamma \gamma {\pi }^0$ signal events. The (black) dots with error bars are the data.

Figure 3

Partial width (in keV) versus $M_{\gamma \gamma }^2$ for the inclusive ${\eta }^{\prime }\to \gamma \gamma {\pi }^0$ decay. The error includes the statistic and systematic uncertainties. The (blue) histogram is the sum of an incoherent mixture of $\rho -\omega$ and the nonresonant components from MC simulations; the (back) dotted-curves is $\omega$-contribution; the (red) dot-dashed-curve is the $\rho$-contribution; and the (green) dashed-curve is the nonresonant contribution. All the components are normalized using the yields obtained in Fig. 4.

Figure 4

Distribution of the invariant mass $M_{\gamma {\pi }^0}$ and fit results in the ${\eta }^{\prime }$ mass region. The points with error bars are data; the (black) dotted-curve is from the $\omega$-contribution; the (red) long dashed-curve is from the $\rho$-contribution; the (blue) short dashed-curve is the contribution of $\rho -\omega$ interference; the (green) long dashed curve is the nonresonance; the (pink) histogram is from the class II background; the (black) short dot-dashed curve is the combinatorial backgrounds of ${\eta }^{\prime }\to \gamma \omega$, $\gamma \rho$. The (blue) solid line shows the total fit function.