Strong decays of low-lying $D$-wave $Ξ_b/Ξ_b'$ baryons with QPC model

Abstract

For further decoding the inner structure of the two excited $Ξ_b$ states observed by LHCb, we perform a systematical study of the strong decays of the low-lying $1D$-wave $Ξ_b$ and $Ξ_b'$ excitations using the quark pair creation model within the $j-j$ coupling scheme. Combining with the measured masses and decay properties of $Ξ_{b}(6327)^{0}$ and $Ξ_{b}(6327)^{0}$, the two excited states can be explained as $1D$ $λ$-mode $Ξ_b$ states $Ξ_{b}|J^{P}=\frac{3}{2}^{+},2\rangle_{λλ}$ and $Ξ_{b}|J^{P}=\frac{5}{2}^{+},2\rangle_{λλ}$, respectively. If such a view were correct, $Ξ_b'π$ and $Ξ_b'^*π$ could be another interesting channels for experimental exploring of the $Ξ_{b}(6327)^{0}$ and $Ξ_{b}(6327)^{0}$, respectively. Those calculations are good consistent with the results within the chiral quark model. In addition, for the other missing $1D$-wave $Ξ_b$ and $Ξ_b'$ excitations, our predictions indicate that:(i) the two $ρ$-mode $1D$ $Ξ_b$ states are likely to be moderate states with a width of $Γ\sim50$ MeV. The $J^P=3/2^+$ state dominantly decays into $Σ_bK$ and $Ξ_b'π$, while the $J^P=5/2^+$ state decays primarily through $Σ_b^*K$ and $Ξ_b'^*π$. (ii) The $λ$-mode $1D$ $Ξ_b'$ states may be moderate states with a widths of about several to dozens of MeV. Most of the $λ$-mode $1D$ $Ξ_b'$ states mainly decay into the $1P$-wave bottomed baryon via the pionic decay processes. Meanwhile, several $λ$-mode $1D$ $Ξ_b'$ states have significant decay rates into $ΛB$. (iii) While, the $ρ$-mode $1D$ $Ξ_b'$ states are predicted to be very broad states with a width of about several hundreds MeV. It will be a great challenge to explore the $ρ$-mode $1D$ $Ξ_b'$ states in experiments for their broad widths.