Molecular states in $D_s^{(\ast )+}{\Xi }_c^{{(}^{\prime },\ast )}$ systems

Abstract

The possible hadronic molecules in $D_s^{(\ast )+}{\Xi }_c^{{(}^{\prime },\ast )}$ systems with $J^P=1/2^{-},3/2^{-}$ and $5/2^{-}$ are investigated with interactions described by light meson exchanges. By varying the cutoff in a phenomenologically reasonable range of $1\sim 2.5$ GeV, we find ten near-threshold (bound or virtual) states in the single-channel case. After introducing the coupled-channel dynamics of $D_s^{+}{\Xi }_c$-$D_s^{+}{\Xi }_c^{{}^{\prime }}$-$D_s^{\ast +}{\Xi }_c$-$D_s^{+}{\Xi }_c^{\ast }$-$D_s^{\ast +}{\Xi }_c^{{}^{\prime }}$-$D_s^{\ast +}{\Xi }_c^{\ast }$ systems, these states, except those below the lowest channels in each $J^P$ sector, move into the complex energy plane and become resonances in the mass range of $4.43\sim 4.76$ GeV. Their spin-parities and nearby thresholds are $1/2^{-}(D_s^{+}{\Xi }_c)$, $1/2^{-}(D_s^{+}{\Xi }_c^{{}^{\prime }})$, $1/2^{-}(D_s^{\ast +}{\Xi }_c)$,$1/2^{-}(D_s^{\ast +}{\Xi }_c^{{}^{\prime }})$, $1/2^{-}(D_s^{\ast +}{\Xi }_c^{\ast })$ , $3/2^{-}(D_s^{\ast +}{\Xi }_c)$, $3/2^{-}(D_s^{+}{\Xi }_c)$, $3/2^{-}(D_s^{\ast +}{\Xi }_c^{{}^{\prime }})$, $3/2^{-}(D_s^{\ast +}{\Xi }_c^{\ast })$, and $5/2^{-}(D_s^{\ast +}{\Xi }_c^{\ast })$. The impacts of the $\delta (r)$-term in the one-boson-exchange model on these states are presented. Setting $\Lambda =1.5$ GeV as an illustrative value, it is found that $1/2^{-}(D_s^{+}{\Xi }_c)$ is a stable bound state (becoming unstable if turning on the coupling to lower channels), $1/2^{-}(D_s^{\ast +}{\Xi }_c)$ and $3/2^{-}(D_s^{\ast +}{\Xi }_c)$ are physical resonances in both cases of including or excluding the $\delta (r)$-term, while the other seven states are physical resonances or ``virtual-state-like" poles near thresholds, depending on including the $\delta (r)$-term or not. In addition, the partial decay widths of the physical resonances are provided. These double-charm hidden-strangeness pentaquark states, as the partners of experimentally observed $P_c$ and $P_{cs}$ states, can be searched for in the $D^{(\ast )}{\Lambda }_c$ final states in future.

arXiv comment15 pages, 6 figures, 9 tables

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