Recoil corrections to pentaquark molecules with an SU(3) anti-triplet heavy baryon

Abstract: Recoil corrections, which appear at order $\mathcal{O}(\frac{1}{M})$, turn out to be crucial for the pentaquark molecules with heavy flavor. In the past, such corrections were typically regarded as negligible for the formation of heavy molecules. However, our research manifests the important impacts on the spectra of possible baryon-meson bound states. In certain cases, the binding energy sharply decreases after considering the recoil corrections. Using the one-boson-exchange (OBE) model, we have studied a series of double heavy and hidden heavy pentaquark states with an SU(3) anti-triplet baryon, including $Ξ{c}\bar{D}^{(*)}$, $Λ{c}\bar{D}^{(*)}$, $Ξ{c}D^{(*)}$, $Λ{c}D^{(*)}$, along with their bottom analogues. Considering both the $S$--{}$D$ wave mixing effect and the recoil corrections, we find that recoil corrections, working against the stability of bound states in certain isospin-singlet channels, which cannot be ignored. For the $Ξ{c}\bar{D}$ and $Ξ{c}D$ systems with $I(J^P)=0(\frac{1}{2}^{-})$, the $Ξ{c}\bar{D}^{*}$ and $Ξ{c}D^{*}$ systems, as well as their bottom counterparts, with $I(J^P)=0(\frac{1}{2}^{-})$ and $0(\frac{3}{2}^{-})$, and the $Λ{b}\bar{B}^{*}$ system with $I(J^P)=\frac{1}{2}(\frac{1}{2}^{-})$ and $\frac{1}{2}(\frac{3}{2}^{-})$, although the bound state solution can be found both with and without considering the recoil corrections, the inclusion of recoil corrections weakens the attraction of the molecules. This phenomenon arising from recoil corrections is especially prominent in the $Ξ{c}\bar{D}^{*}$ and $Ξ_{c}D^{*}$ systems.