Strong decays of the ${\mathrm{\Xi }}_b(6227)$ as a ${\mathrm{\Sigma }}_b\overline{K}$ molecule

We study the strong decays of the newly observed ${\mathrm{\Xi }}_b(6227)$ assuming that it is a pure ${\mathrm{\Sigma }}_b\overline{K}$ molecular state. Considering four possible spin-parity assingments $J^P=1/2^{\pm }$ and $3/2^{\pm }$, the partial decay widths of the ${\mathrm{\Sigma }}_b\overline{K}$ molecular state into ${\mathrm{\Lambda }}_b\overline{K}$, ${\mathrm{\Xi }}_b\pi$, and ${\mathrm{\Xi }}_b^{\prime }\pi$ final states through hadronic loops are evaluated with the help of the effective Lagrangians. In comparison with the LHCb data, the spin-party $1/2^{-}$ assignment is preferred while those of $J^P=1/2^{+}$ and $J^P=3/2^{\pm }$ are disfavored. In addition, we show that the two allowed decay modes ${\mathrm{\Lambda }}_b\overline{K}$ and ${\mathrm{\Xi }}_b\pi$ of the ${\mathrm{\Xi }}_b(6227)$, being a $S$-wave ${\mathrm{\Sigma }}_b\overline{K}$ molecular state, have almost equal branching ratios.

Figure 1

Self-energy of the ${\mathrm{\Xi }}_b^{*}$ state.

Figure 2

Feynman diagrams for the ${\mathrm{\Xi }}_b^{*-}\to {\mathrm{\Lambda }}_b^0{K}^{-}$,${\mathrm{\Xi }}_b^0{\pi }^{-}$, and ${\mathrm{\Xi }}_b^{\prime 0}{\pi }^{-}$ decay processes. We also show the definitions of the kinematics ($k_0$, $k_1$, $k_2$, $p_1$, $p_2$, and $q$) used in the calculation.

Figure 3

The coupling constants of the ${\mathrm{\Xi }}_b^{*}$ state with different $J^P$ assignments as a function of the parameter $\mathrm{\Lambda }$.

Figure 4

Partial decay widths of the ${\mathrm{\Xi }}_b^{*}\to {\mathrm{\Lambda }}_b\overline{K}$ (blue dashed lines), ${\mathrm{\Xi }}_b^{*}\to {\mathrm{\Xi }}_b\pi$ (red dotted lines), ${\mathrm{\Xi }}_b^{*}\to {\mathrm{\Xi }}_b^{\prime }\pi$ (green dash-dotted lines), and the total decay width (black solid lines) with different spin-parity assignments for the ${\mathrm{\Xi }}_b^{*}$ as a function of the parameter $\mathrm{\Lambda }$. The cyan bands denote the experimental total width [4].

Figure 5

Ratio of the partial decay widths $B({\mathrm{\Xi }}_b^{*}\to {\mathrm{\Lambda }}_b\overline{K})/B({\mathrm{\Xi }}_b^{*}\to {\mathrm{\Xi }}_b\pi )$ for different spin-parity assignments. The cyan band denotes that the ratio is about 0.5–1.5 and is cited from Ref. [4].