Nature of the $P_c$ states from compositeness criteria
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912641880948736 |
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| author | Wang, Yu-Fei Shen, Chao-Wei Rönchen, Deborah Meißner, Ulf-G. Zou, Bing-Song Huang, Fei |
| author_facet | Wang, Yu-Fei Shen, Chao-Wei Rönchen, Deborah Meißner, Ulf-G. Zou, Bing-Song Huang, Fei |
| contents | Based on a coupled-channel approach, we investigate the structures of four $P_c$ states through compositeness criteria. Toward a more precise description of the states, we have obtained refined fit results of the LHCb data on the $J/ψp$ invariant mass distribution of the $Λ_b^0\to J/ψp K^-$ decay. Allowing for the fact that each of the four $P_c$ states couples strongly to a nearby $S$-wave channel, three criteria on the compositeness/elementariness are adopted in this study: the pole-counting rule, the spectral density function, and the Gamow wave function. Compositeness information is extracted from the scattering amplitudes and the pole parameters (pole positions and residues), without any preconceived assumptions on the nature of the $P_c$ states, and without any dependence on the model parametrization. Consistently within the framework of all the three methods, it has been found that the $P_c(4312)\,1/2^-$ is mainly composed by $\bar{D}Σ_c$, $P_c(4380)\,3/2^-$ by $\bar{D}Σ_c^*$, while the $P_c(4440)\,1/2^-$ and $P_c(4457)\,3/2^-$ states both turn out as composite states of $\bar{D}^*Σ_c$. The upper limits of the values of their elementariness are estimated to be rather small. This paper provides an additional confirmation of the molecular interpretation for the $P_c$ states in the literature. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_21858 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nature of the $P_c$ states from compositeness criteria Wang, Yu-Fei Shen, Chao-Wei Rönchen, Deborah Meißner, Ulf-G. Zou, Bing-Song Huang, Fei High Energy Physics - Phenomenology High Energy Physics - Theory Nuclear Theory Based on a coupled-channel approach, we investigate the structures of four $P_c$ states through compositeness criteria. Toward a more precise description of the states, we have obtained refined fit results of the LHCb data on the $J/ψp$ invariant mass distribution of the $Λ_b^0\to J/ψp K^-$ decay. Allowing for the fact that each of the four $P_c$ states couples strongly to a nearby $S$-wave channel, three criteria on the compositeness/elementariness are adopted in this study: the pole-counting rule, the spectral density function, and the Gamow wave function. Compositeness information is extracted from the scattering amplitudes and the pole parameters (pole positions and residues), without any preconceived assumptions on the nature of the $P_c$ states, and without any dependence on the model parametrization. Consistently within the framework of all the three methods, it has been found that the $P_c(4312)\,1/2^-$ is mainly composed by $\bar{D}Σ_c$, $P_c(4380)\,3/2^-$ by $\bar{D}Σ_c^*$, while the $P_c(4440)\,1/2^-$ and $P_c(4457)\,3/2^-$ states both turn out as composite states of $\bar{D}^*Σ_c$. The upper limits of the values of their elementariness are estimated to be rather small. This paper provides an additional confirmation of the molecular interpretation for the $P_c$ states in the literature. |
| title | Nature of the $P_c$ states from compositeness criteria |
| topic | High Energy Physics - Phenomenology High Energy Physics - Theory Nuclear Theory |
| url | https://arxiv.org/abs/2506.21858 |