First observation of the decay ${\chi }_{cJ}\to {\mathrm{\Sigma }}^{+}\overline{p}{K}_S^0+\mathrm{c}.\mathrm{c}.\mathbf{(}J=0,1,2\mathbf{)}$

Using E1 radiative transitions $\psi (3686)\to \gamma {\chi }_{cJ}$ from a sample of $(448.1\pm 2.9)\times {10}^6\psi (3686)$ events collected with the BESIII detector, the decays ${\chi }_{cJ}\to {\mathrm{\Sigma }}^{+}\overline{p}{K}_S^0+\mathrm{c}.\mathrm{c}.(J=0,1,2)$ are studied. The decay branching fractions are measured to be $\mathcal{B}({\chi }_{c0}\to {\mathrm{\Sigma }}^{+}\overline{p}{K}_S^0+\mathrm{c}.\mathrm{c}.)=(3.52\pm 0.19\pm 0.21)\times {10}^{-4}$, $\mathcal{B}({\chi }_{c1}\to {\mathrm{\Sigma }}^{+}\overline{p}{K}_S^0+\mathrm{c}.\mathrm{c}.)=(1.53\pm 0.10\pm 0.08)\times {10}^{-4}$, and $\mathcal{B}({\chi }_{c2}\to {\mathrm{\Sigma }}^{+}\overline{p}{K}_S^0+\mathrm{c}.\mathrm{c}.)=(8.25\pm 0.83\pm 0.49)\times {10}^{-5}$, where the first and second uncertainties are the statistical and systematic ones, respectively. No evident intermediate resonances are observed in the studied processes.

Figure 1

The distribution of the ${\pi }^{+}{\pi }^{-}$ invariant mass versus the $p{\pi }^0$ invariant mass. The black solid box in the center is the signal region, the blue long dashed boxes show the $K_S^0$ and ${\mathrm{\Sigma }}^{+}$ mass sideband regions, and the green dashed boxes are the events from non-$K_S^0$ and non-${\mathrm{\Sigma }}^{+}$ candidates.

Figure 2

The ${\mathrm{\Sigma }}^{+}\overline{p}{K}_S^0$ invariant-mass distribution in the vicinity of the ${\chi }_{cJ}$ states. Dots with error bars are data, the red solid line histogram is the ${\chi }_{cJ}$ line shape from the MC simulation, and the arrows indicate the ${\chi }_{c0}$, ${\chi }_{c1}$, and ${\chi }_{c2}$ signal regions.

Figure 3

The $\overline{p}{K}_S^0$ invariant-mass distributions in the (a) ${\chi }_{c0}$, (b) ${\chi }_{c1}$, and (c) ${\chi }_{c2}$ signal regions. The dots with error bars are data, and the red lines are the contributions from the corresponding MC simulations based on the phase-space model. For panel (a), the black solid line is the fit result, the blue long-dashed curve is the contribution from ${\chi }_{c0}\to {\mathrm{\Sigma }}^{+}\overline{\mathrm{\Sigma }}(1940{)}^{-}$, and the green solid line is the contribution from the normalized $K_S^0$ and ${\mathrm{\Sigma }}^{+}$ mass sideband regions.

Figure 4

The ${\mathrm{\Sigma }}^{+}{K}_S^0$ and ${\mathrm{\Sigma }}^{+}\overline{p}$ invariant-mass distributions in the (a)–(b) ${\chi }_{c0}$, (c)–(d) ${\chi }_{c1}$, and (e)–(f) ${\chi }_{c2}$ signal regions. The dots with error bars are data, and the red lines are the contributions from the corresponding MC simulations based on the phase-space model.

Figure 5

Fit to the ${\mathrm{\Sigma }}^{+}\overline{p}{K}_S^0$ invariant-mass distribution in the ${\chi }_{cJ}$ mass region of $[3.3,3.6]\mathrm{GeV}/c^2$. Dots with error bars are data, the red solid curve shows the result of the unbinned maximum-likelihood fit, the green-shaded histograms are the events from the normalized $K_S^0$ and ${\mathrm{\Sigma }}^{+}$ mass sidebands, the blue solid line is the sum of the peaking and flat background components, and the violet long dashed curve is the contribution of the peaking background normalized according to the sideband events.