Theoretical study of the $\mathrm{\Xi }\left(1620\right)$ and $\mathrm{\Xi }\left(1690\right)$ resonances in ${\mathrm{\Xi }}_c\to {\pi }^{+}\mathit{MB}$ decays

Nonleptonic weak decays of ${\mathrm{\Xi }}_c$ into ${\pi }^{+}$ and a meson $\left(M\right)$-baryon $\left(B\right)$ final state, $MB$, are analyzed from the viewpoint of probing $S=-2$ baryon resonances, i.e., $\mathrm{\Xi }\left(1620\right)$ and $\mathrm{\Xi }\left(1690\right)$, of which spin-parity and other properties are not well known. We argue that the weak decay of ${\mathrm{\Xi }}_c$ is dominated by a single quark-line diagram, preferred by the Cabibbo-Kobayashi-Maskawa coefficient, color recombination factor, the diquark correlation, and the kinematical condition. The decay process has an advantage of being free from meson resonances in the ${\pi }^{+}M$ invariant mass distribution. The invariant mass distribution of the meson-baryon final state is calculated with three different chiral unitary approaches, assuming that the $\mathrm{\Xi }\left(1620\right)$ and $\mathrm{\Xi }\left(1690\right)$ resonances have $J^P=1/2^{-}$. It is found that a clear peak for the $\mathrm{\Xi }\left(1690\right)$ is seen in the $\pi \mathrm{\Xi }$ and $\overline{K}\mathrm{\Lambda }$ spectra. We also suggest that the ratios of the $\pi \mathrm{\Xi },\overline{K}\mathrm{\Lambda }$, and $\overline{K}\mathrm{\Sigma }$ final states are useful to distinguish whether the peak is originated from the $\mathrm{\Xi }\left(1690\right)$ resonance or it is a $\overline{K}\mathrm{\Sigma }$ threshold effect.

Figure 1

$M_{\overline{K}\mathrm{\Lambda }}^2$ and $M_{K^{+}\overline{K}}^2$ Dalitz plot for the ${\mathrm{\Lambda }}_c\to K^{+}\left(\overline{K}\mathrm{\Lambda }\right)$ reaction. The $\mathrm{\Xi }\left(1690\right)$ energy is shown by the vertical dotted line, while the horizontal band represents the mass and the width of the $a_0\left(980\right)$.

Figure 2

$M_{\overline{K}\mathrm{\Lambda }}^2$ and $M_{{\pi }^{+}\overline{K}}^2$ Dalitz plot for the ${\mathrm{\Xi }}_c\to {\pi }^{+}\left(\overline{K}\mathrm{\Lambda }\right)$ reaction. As in Fig. 1, the $\mathrm{\Xi }\left(1690\right)$ energy is shown by the vertical dotted line. The horizontal band represents the mass and the width of the $K^{*}\left(892\right)$.

Figure 3

Dominant quark-line diagram for the ${\mathrm{\Xi }}_c^{+}\to {\pi }^{+}MB$ decay. The solid and the wiggly lines stand for the quarks and the $W$ boson, respectively.

Figure 4

Subdominant mechanism for the ${\mathrm{\Xi }}_c^{+}\to {\pi }^{+}MB$ decay. Though its contribution is also Cabibbo allowed, it is however suppressed when compared to that depicted in Fig. 3 (see text for details).

Figure 5

Other possible mechanisms for the ${\mathrm{\Xi }}_c^{+}\to {\pi }^{+}MB$ decay.

Figure 6

Schematic diagram for the FSI of the meson-baryon pair (solid circle). The first and the second terms in the right-hand side stand for the tree and the rescattering contributions, respectively. The latter diagram contains the meson-baryon loop function $G$ and the scattering amplitude $t$. Besides, the factor $h$ represents the intermediate meson-baryon weight introduced in Eqs. (4) or (5).

Figure 7

${\pi }^0{\mathrm{\Xi }}^0$ invariant mass distribution obtained with the ROB (red dashed curve) and the GLN (black solid curve) models. The vertical lines represent the $\overline{K}\mathrm{\Lambda }$ and $\overline{K}\mathrm{\Sigma }$ thresholds.

Figure 8

${\overline{K}}^0\mathrm{\Lambda }$ (black solid curve), $K^{-}{\mathrm{\Sigma }}^{+}$ (red dash-dotted curve), and ${\pi }^0{\mathrm{\Xi }}^0$ (blue dotted curve) invariant mass distributions obtained with the GLN chiral unitary approach. The vertical dashed line marks the $\overline{K}\mathrm{\Sigma }$ threshold.

Figure 9

${\overline{K}}^0\mathrm{\Lambda }$ (black solid curve), $K^{-}{\mathrm{\Sigma }}^{+}$ (red dash-dotted curve) and ${\pi }^0{\mathrm{\Xi }}^0$ (blue dotted curve) invariant mass distributions obtained with the Sekihara model of Ref. [44]. The vertical dashed lines mark the $K^{-}{\mathrm{\Sigma }}^{+}$ and ${\overline{K}}^0{\mathrm{\Sigma }}^0$ thresholds.

Figure 10

${\overline{K}}^0\mathrm{\Lambda }$ (black solid curve), $K^{-}{\mathrm{\Sigma }}^{+}$ (red dash-dotted curve), and ${\pi }^0{\mathrm{\Xi }}^0$ (blue dotted curve) invariant mass distributions obtained with the ROB model. The vertical dashed line indicates the $\overline{K}\mathrm{\Sigma }$ threshold.

Figure 11

(a) ${\pi }^0{\mathrm{\Xi }}^0$, (b) ${\overline{K}}^0\mathrm{\Lambda }$, and (c) $K^{-}{\mathrm{\Sigma }}^{+}$ invariant mass distributions obtained in the Sekihara model using three different values of $x=0$ (black solid curves), $+1$ (red dash-dotted curves), and $-1$ (blue dotted curves). The weight $x$ is defined in Eq. (7) and controls the amount of the $\eta \mathrm{\Xi }$ component in the intermediate $MB$ state.

Figure 12

Cabibbo favored quark-line diagrams for the ${\mathrm{\Xi }}_c^{+}\to {\pi }^{+}\left(ssu\right)$ and ${\mathrm{\Xi }}_c^0\to {\pi }^{+}\left(ssd\right)$ decays.