Observation of $h_c$ Radiative Decay $h_c\to \gamma {\eta }^{\prime }$ and Evidence for $h_c\to \gamma \eta$

A search for radiative decays of the $P$-wave spin singlet charmonium resonance $h_c$ is performed based on $4.48\times {10}^8$ ${\psi }^{\prime }$ events collected with the BESIII detector operating at the BEPCII storage ring. Events of the reaction channels $h_c\to \gamma {\eta }^{\prime }$ and $\gamma \eta$ are observed with a statistical significance of $8.4\sigma$ and $4.0\sigma$, respectively, for the first time. The branching fractions of $h_c\to \gamma {\eta }^{\prime }$ and $h_c\to \gamma \eta$ are measured to be $\mathcal{B}(h_c\to \gamma {\eta }^{\prime })=(1.52\pm 0.27\pm 0.29)\times {10}^{-3}$ and $\mathcal{B}(h_c\to \gamma \eta )=(4.7\pm 1.5\pm 1.4)\times {10}^{-4}$, respectively, where the first errors are statistical and the second are systematic uncertainties.

Figure 1

Scatter plots of the selected events from the ${\psi }^{\prime }$ data set. (a) $M({\eta }^{\prime }\to {\pi }^{+}{\pi }^{-}\eta )$ versus $M(\gamma {\pi }^{+}{\pi }^{-}\eta )$ for $h_c\to \gamma {\eta }^{\prime }({\eta }^{\prime }\to {\pi }^{+}{\pi }^{-}\eta )$. (b) $M({\eta }^{\prime }\to \gamma {\pi }^{+}{\pi }^{-})$ versus $M(\gamma \gamma {\pi }^{+}{\pi }^{-})$ for $h_c\to \gamma {\eta }^{\prime }({\eta }^{\prime }\to \gamma {\pi }^{+}{\pi }^{-})$. (c) $M(\eta \to \gamma \gamma )$ versus $M(\gamma \gamma \gamma )$ for $h_c\to \gamma \eta (\eta \to \gamma \gamma )$. (d) $M(\eta \to {\pi }^{+}{\pi }^{-}{\pi }^0)$ versus $M(\gamma {\pi }^{+}{\pi }^{-}{\pi }^0)$ for $h_c\to \gamma \eta (\eta \to {\pi }^{+}{\pi }^{-}{\pi }^0)$. The blue dashed lines mark the signal region of ${\eta }^{\prime }$ $(\eta )$ and the red dashed lines mark the nominal $h_c$ mass.

Figure 2

Results of the simultaneous fits to the two invariant mass distributions of (top) $M(\gamma {\eta }^{\prime })$ and (below) $M(\gamma \eta )$ for data. (a) $M(\gamma {\eta }^{\prime })$ distribution for $h_c\to \gamma {\eta }^{\prime }({\eta }^{\prime }\to {\pi }^{+}{\pi }^{-}\eta )$. (b) $M(\gamma {\eta }^{\prime })$ distribution for $h_c\to \gamma {\eta }^{\prime }({\eta }^{\prime }\to \gamma {\pi }^{+}{\pi }^{-})$. (c) $M(\gamma \eta )$ distribution for $h_c\to \gamma \eta (\eta \to \gamma \gamma )$. (d) $M(\gamma \eta )$ distribution for $h_c\to \gamma \eta (\eta \to {\pi }^{+}{\pi }^{-}{\pi }^0)$. The red solid curves are the fit results, the blue dashed curves are the background distributions, and the green hatched histograms are events from the ${\eta }^{\prime }(\eta )$ sidebands.