Study of excited $\mathrm{\Xi }$ states in $\psi (3686)\to K^{-}\mathrm{\Lambda }{\overline{\mathrm{\Xi }}}^{+}+\mathrm{c}.\mathrm{c}.$

Based on a sample of $(448.1\pm 2.9)\times {10}^6$ $\psi (3686)$ events collected with the BESIII detector at BEPCII, the decays of $\psi (3686)\to K^{-}\mathrm{\Lambda }{\overline{\mathrm{\Xi }}}^{+}+\mathrm{c}.\mathrm{c}.$ with ${\overline{\mathrm{\Xi }}}^{+}\to \overline{\mathrm{\Lambda }}{\pi }^{+}$, $\overline{\mathrm{\Lambda }}\to \overline{p}{\pi }^{+}$ are studied. We investigate the two excited resonances, $\mathrm{\Xi }(1690{)}^{-}$ and $\mathrm{\Xi }(1820{)}^{-}$, which are each observed with large significance ($\gg 10\sigma$) in the $K^{-}\mathrm{\Lambda }$ invariant mass distributions. A partial wave analysis is performed, and the spin-parities of $\mathrm{\Xi }(1690{)}^{-}$ and $\mathrm{\Xi }(1820{)}^{-}$ are measured to be ${\frac{1}{2}}^{-}$ and ${\frac{3}{2}}^{-}$, respectively. The masses, widths, and product branching fractions of $\mathrm{\Xi }(1690{)}^{-}$ and $\mathrm{\Xi }(1820{)}^{-}$ are also measured.

Figure 1

Distribution of $M(\overline{p}{\pi }^{+})$ of $\overline{\mathrm{\Lambda }}$ candidates (a), decay length of ${\overline{\mathrm{\Xi }}}^{+}$ candidates (b), and $M(\overline{\mathrm{\Lambda }}{\pi }^{+})$ of ${\overline{\mathrm{\Xi }}}^{+}$ candidates (c). Plot (d) shows the distribution of $\mathrm{RM}(K^{-}{\overline{\mathrm{\Xi }}}^{+})$: the left peak is $\mathrm{\Lambda }$, while the right one is ${\mathrm{\Sigma }}^0$. The crosses represent data and the histograms represent phase space (PHSP) MC. The dashed arrows show the cut values; for each plot, cuts on the other three quantities are applied.

Figure 2

(a) Dalitz plot of $M^2(\mathrm{\Lambda }{\overline{\mathrm{\Xi }}}^{+})\mathrm{vs}{M}^2(K^{-}{\overline{\mathrm{\Xi }}}^{+})$ and the distributions of (b) $M(K^{-}\mathrm{\Lambda })$, (c) $M(K^{-}{\overline{\mathrm{\Xi }}}^{+})$ and (d) $M(\mathrm{\Lambda }{\overline{\mathrm{\Xi }}}^{+})$ after the final selection. The crosses represent the data and the histograms represent the background events estimated from the $\mathrm{\Xi }$ sidebands.

Figure 3

Distributions of (a) $M(K^{-}{\overline{\mathrm{\Xi }}}^{+})$, (b) $M(\mathrm{\Lambda }{\overline{\mathrm{\Xi }}}^{+})$, and (c) $M(K^{-}\mathrm{\Lambda })$. The crosses represent data and red solid histograms represent the projection of the PWA result. The different color histograms represent the intensity of each component in the nominal fit. Here, ${\chi }^2/\mathrm{nbin}$ demonstrates the goodness of fit in each figure, where nbin is the number of bins in each figure and ${\chi }^2$ is defined as ${\chi }^2={\sum }_{i=1}^{\mathrm{nbin}}(n_i-v_i{)}^2/v_i$, where $n_i$ and $v_i$ are the numbers of events for the data and the fit projections of the nominal fit in the $i$th interval of each figure, respectively.

Figure 4

Fit to the $\mathrm{RM}(K^{-}{\overline{\mathrm{\Xi }}}^{+})$ distribution. The crosses are data and the red curve denotes the best fit. The other curves show the different fit components listed in the legend.