Strong decays of $P_ψ^N(4440)^+$ and $P_ψ^N(4457)^+$ within the Bethe-Salpeter framework
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2025
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| author | Li, Qiang Chang, Chao-Hsi Tong, Xin Tan, Xiao-Ze Wang, Tianhong Wang, Guo-Li |
| author_facet | Li, Qiang Chang, Chao-Hsi Tong, Xin Tan, Xiao-Ze Wang, Tianhong Wang, Guo-Li |
| contents | By combining the effective Lagrangian and Bethe-Salpeter framework, we studied the mass spectra, wave functions, and strong decay widths of the two pentaquark states $P_ψ^N(4440)^+$ and $P_ψ^N(4457)^+$ reported by LHCb in 2019. Taking into account both the mass ordering and the decay widths, our results favor the interpretation of $P_ψ^N(4440)^+$ and $P_ψ^N(4457)^+$ as the isospin-$\frac12$ $[\bar D^*Σ_c]$ molecular states with $J^P$ configuration $(\frac{3}{2})^-$ and $(\frac12)^-$, respectively. We first calculate the one-boson-exchange interaction kernel of $[\bar D^*Σ_c]$ in the isospin-$\frac12$ configuration. Then we present the Bethe-Salpeter equation (BSE) and wave functions for the bound states of a vector meson and a $\frac12$ baryon with $J^P={\frac12}^-$ and ${\frac32}^-$. The obtained mass results for the $(\frac32)^-$ and $(\frac12)^-$ are $4.442$ and $4.457$ GeV, respectively. Combining the effective Lagrangians and the BS wave functions, we further calculate the strong decay channels $\bar D^{(*)0}Λ_c^+$, $J/ψ(η_c) p$, and $\bar DΣ_c^{(*)}$ for the two $P_ψ^N$ states. In the favored $\frac32^-$ and $\frac12^-$ configuration, the obtained total widths are $21.8$ MeV and $13.0$ MeV, respectively, which are substantially consistent with the LHCb data. Our results suggest that $\bar D^{0}Λ_c^+$ and $\bar D^{(*)0}Λ_c^+$ are the dominant decay channels to detect $P_ψ^N(4440)^+$ and $P_ψ^N(4457)^+$, respectively. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_08440 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Strong decays of $P_ψ^N(4440)^+$ and $P_ψ^N(4457)^+$ within the Bethe-Salpeter framework Li, Qiang Chang, Chao-Hsi Tong, Xin Tan, Xiao-Ze Wang, Tianhong Wang, Guo-Li High Energy Physics - Phenomenology High Energy Physics - Experiment High Energy Physics - Lattice By combining the effective Lagrangian and Bethe-Salpeter framework, we studied the mass spectra, wave functions, and strong decay widths of the two pentaquark states $P_ψ^N(4440)^+$ and $P_ψ^N(4457)^+$ reported by LHCb in 2019. Taking into account both the mass ordering and the decay widths, our results favor the interpretation of $P_ψ^N(4440)^+$ and $P_ψ^N(4457)^+$ as the isospin-$\frac12$ $[\bar D^*Σ_c]$ molecular states with $J^P$ configuration $(\frac{3}{2})^-$ and $(\frac12)^-$, respectively. We first calculate the one-boson-exchange interaction kernel of $[\bar D^*Σ_c]$ in the isospin-$\frac12$ configuration. Then we present the Bethe-Salpeter equation (BSE) and wave functions for the bound states of a vector meson and a $\frac12$ baryon with $J^P={\frac12}^-$ and ${\frac32}^-$. The obtained mass results for the $(\frac32)^-$ and $(\frac12)^-$ are $4.442$ and $4.457$ GeV, respectively. Combining the effective Lagrangians and the BS wave functions, we further calculate the strong decay channels $\bar D^{(*)0}Λ_c^+$, $J/ψ(η_c) p$, and $\bar DΣ_c^{(*)}$ for the two $P_ψ^N$ states. In the favored $\frac32^-$ and $\frac12^-$ configuration, the obtained total widths are $21.8$ MeV and $13.0$ MeV, respectively, which are substantially consistent with the LHCb data. Our results suggest that $\bar D^{0}Λ_c^+$ and $\bar D^{(*)0}Λ_c^+$ are the dominant decay channels to detect $P_ψ^N(4440)^+$ and $P_ψ^N(4457)^+$, respectively. |
| title | Strong decays of $P_ψ^N(4440)^+$ and $P_ψ^N(4457)^+$ within the Bethe-Salpeter framework |
| topic | High Energy Physics - Phenomenology High Energy Physics - Experiment High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2503.08440 |