Study of $h_c\to 3({\pi }^{+}{\pi }^{-}){\pi }^0$, $h_c\to 2({\pi }^{+}{\pi }^{-})\omega$, $h_c\to 2({\pi }^{+}{\pi }^{-}){\pi }^0\eta$, $h_c\to 2({\pi }^{+}{\pi }^{-})\eta$, and $h_c\to p\overline{p}$

Based on $(2712.4\pm 14.1)\times {10}^6$ $\psi (3686)$ events collected with the BESIII detector, we study the decays $h_c\to 3({\pi }^{+}{\pi }^{-}){\pi }^0$, $h_c\to 2({\pi }^{+}{\pi }^{-})\omega$, $h_c\to 2({\pi }^{+}{\pi }^{-}){\pi }^0\eta$, $h_c\to 2({\pi }^{+}{\pi }^{-})\eta$, and $h_c\to p\overline{p}$ via $\psi (3686)\to {\pi }^0{h}_c$. The decay channel $h_c\to 3({\pi }^{+}{\pi }^{-}){\pi }^0$ is observed for the first time, and its branching fraction is determined to be $(9.28\pm 1.14\pm 0.77)\times {10}^{-3}$, where the first uncertainty is statistical and the second is systematic. In addition, first evidence is found for the modes $h_c\to 2({\pi }^{+}{\pi }^{-}){\pi }^0\eta$ and $h_c\to 2({\pi }^{+}{\pi }^{-})\omega$ with significances of $4.8\sigma$ and $4.7\sigma$, and their branching fractions are determined to be $(7.55\pm 1.51\pm 0.77)\times {10}^{-3}$ and $(4.00\pm 0.86\pm 0.35)\times {10}^{-3}$, respectively. No significant signals of $h_c\to 2({\pi }^{+}{\pi }^{-})\eta$ and $h_c\to p\overline{p}$ are observed, and the upper limits of the branching fractions of these decays are determined to be $<6.19\times {10}^{-4}$ and $<4.40\times {10}^{-5}$ at the 90% confidence level, respectively.

Figure 1

The $M_{{\pi }^{+}{\pi }^{-}{\pi }_H^0}$ distribution of the accepted candidates in data. The dotted error bars represent the distribution of different ${\pi }^{+}{\pi }^{-}{\pi }_H^0$ combinations overlaid. The pair of red arrows show the $\omega$ signal region, and the pair of green arrows show the $\omega$ sideband region.

Figure 2

Fits to the invariant-mass distributions of (a) $h_c\to 3({\pi }^{+}{\pi }^{-}){\pi }^0$, (b) $h_c\to 2({\pi }^{+}{\pi }^{-}){\pi }^0\eta$, (c) $h_c\to 2({\pi }^{+}{\pi }^{-})\eta$, (d) $h_c\to p\overline{p}$, (e) $h_c\to 2({\pi }^{+}{\pi }^{-})\omega$ in the $\omega$ signal region, and (f) $h_c\to 3({\pi }^{+}{\pi }^{-}){\pi }^0$ in the $\omega$ sideband region. The green histogram shows the scaled $h_c$ peak obtained from the fit to the events inside the $\omega$ sideband region. The lower panels of each plot show the fit residuals expressed in number of standard deviations.

Figure 3

The normalized likelihood distribution for (left) $h_c\to 2({\pi }^{+}{\pi }^{-})\eta$ and (right) $h_c\to p\overline{p}$ mode. The results obtained with and without incorporating the systematic uncertainties are shown in blue dots and black dots, respectively. The arrow is the position of the upper limit on the signal yields at 90% confidence level.