First observation of the decays ${\chi }_{cJ}\to {\pi }^0{\pi }^0{\pi }^0{\pi }^0$

We present a study of the $P$-wave spin-triplet charmonium ${\chi }_{cJ}$ decays ($J=0$, 1, 2) into ${\pi }^0{\pi }^0{\pi }^0{\pi }^0$. The analysis is based on $106\times {10}^6$ ${\psi }^{\prime }$ decays recorded with the BESIII detector at the BEPCII electron positron collider. The decay into the ${\pi }^0{\pi }^0{\pi }^0{\pi }^0$ hadronic final state is observed for the first time. We measure the branching fractions $B({\chi }_{c0}\to {\pi }^0{\pi }^0{\pi }^0{\pi }^0)=(3.34\pm 0.06\pm 0.44)\times {10}^{-3}$, $B({\chi }_{c1}\to {\pi }^0{\pi }^0{\pi }^0{\pi }^0)=(0.57\pm 0.03\pm 0.08)\times {10}^{-3}$, and $B({\chi }_{c2}\to {\pi }^0{\pi }^0{\pi }^0{\pi }^0)=(1.21\pm 0.05\pm 0.16)\times {10}^{-3}$, where the uncertainties are statistical and systematical, respectively.

Figure 1

Invariant $\gamma \gamma$ mass distribution of all photon pair combinations for selected $9\gamma$ events. The arrows indicate the mass window used for the selection of ${\pi }^0$ candidates.

Figure 2

The spectrum of the energy $E_{\gamma }^{*}$ of the radiative photon from ${\psi }^{\prime }\to \gamma {\chi }_{cJ}$ with the result of the fit (solid curve) described in the text. The dashed curve shows the background line shape and the dotted curves represent the signal line shapes derived from MC simulations (see Sec. 5).

Figure 3

Shown is the invariant di-${\pi }^0$ mass plotted versus the other invariant di-${\pi }^0$ mass for events selected from the (a) ${\chi }_{c0}$, (b) ${\chi }_{c1}$, and (c) ${\chi }_{c2}$ signal regions. All possible ${\pi }^0{\pi }^0$ combinations of the ${\pi }^0{\pi }^0{\pi }^0{\pi }^0$ hadronic final state are plotted. In addition the plots are symmetrized; thus, each event enters 6 times to the plots. The one-dimensional projections are shown in (d), (e), and (f) for ${\chi }_{c0}$, ${\chi }_{c1}$, and ${\chi }_{c2}$, respectively, where the dots with error bars show the data and the shaded histograms show the di-${\pi }^0$ mass distributions obtained from signal MC events simulated without intermediate resonances for the ${\chi }_{cJ}$ decays.