Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

Xiao Chen, Li Ma

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.

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

Abstract

Recoil corrections, which appear at order , 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 , , , , along with their bottom analogues. Considering both the \--{} 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 and systems with , the and systems, as well as their bottom counterparts, with and , and the system with and , 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 and systems.
Paper Structure (16 sections, 20 equations, 6 figures, 9 tables)

This paper contains 16 sections, 20 equations, 6 figures, 9 tables.

Table of Contents

  1. Introduction
  2. Formalism
  3. Wave functions
  4. Relativistic effective Lagrangians and Effective potentials
  5. Numerical results
  6. The mass spectra of $\Xi_{c}\bar{D}^{(*)}$ systems
  7. The mass spectra of $\Xi_{c}D^{(*)}$ systems
  8. The mass spectra of $\Lambda_{c}\bar{D}^{(*)}$ and $\Lambda_{c}D^{(*)}$ systems
  9. The mass spectra of $\Xi_{b}B^{(*)}$ and $\Xi_{b}\bar{B}^{(*)}$ systems
  10. The mass spectra of $\Lambda_{b}B^{(*)}$ and $\Lambda_{b}\bar{B}^{(*)}$ systems
  11. Summary and Discussion
  12. Acknowledgment
  13. Appendix
  14. Fourier transformations of bold q and bold k related structures
  15. Representations of momentum-related operators
  16. ...and 1 more sections

Figures (6)

  • Figure 1: The effective potentials for the $\Xi_{c}\bar{D}$ system in the $0(\frac{1}{2}^{-})$channel. Panel (a): contributions from $\sigma$, $\rho$, and $\omega$ exchange without recoil corrections. Panel (b): same with recoil corrections. The cutoff value is $\Lambda=1.75$ GeV.
  • Figure 2: The effective potentials for the $\Xi_{c}\bar{D}^{*}$ system in the $0(\frac{1}{2}^{-})$ (upper row) and $0(\frac{3}{2}^{-})$ (lower row) channels. Panels (a,d): contributions from $\sigma$, $\rho$, and $\omega$ exchange without recoil corrections. Panels (b,e): same with recoil corrections. Panels (c,f): comparison of the total potentials in the ground state with and without recoil corrections. The cutoff value is $\Lambda=1.75$ GeV.
  • Figure 3: The effective potentials for the $\Xi_{c}D$ system in the $0(\frac{1}{2}^{-})$channel. Panel (a): contributions from $\sigma$, $\rho$, and $\omega$ exchange without recoil corrections. Panel (b): same with recoil corrections. The cutoff value is $\Lambda=1.45$ GeV.
  • Figure 4: The effective potentials for the $\Xi_{c}D^{*}$ system in the $0(\frac{1}{2}^{-})$ (upper row) and $0(\frac{3}{2}^{-})$ (lower row) channels. Panels (a,d): contributions from $\sigma$, $\rho$, and $\omega$ exchange without recoil corrections. Panels (b,e): same with recoil corrections. Panels (c,f): comparison of the total potentials in the ground state with and without recoil corrections. The cutoff value is $\Lambda=1.45$ GeV.
  • Figure 5: The effective potentials for the $\Lambda_{b}\bar{B}$ system in the $\frac{1}{2}(\frac{1}{2}^{-})$channel. Panel (a): contributions from $\sigma$ and $\omega$ exchange without recoil corrections. Panel (b): same with recoil corrections. The cutoff value is $\Lambda=1.70$ GeV.
  • ...and 1 more figures