Scattering lengths of the $J/ψπ$ and $J/ψK$ systems
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| Format: | Preprint |
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2026
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| _version_ | 1866915755516231680 |
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| author | Yan, Jiang Cao, Xiong-Hui Du, Meng-Lin Guo, Feng-Kun |
| author_facet | Yan, Jiang Cao, Xiong-Hui Du, Meng-Lin Guo, Feng-Kun |
| contents | We investigate the low-energy interactions between the charmonium state $J/ψ$ and the light pseudoscalar mesons ($π$ and $K$) within the framework of dispersion relations.We demonstrate that the symmetry-breaking terms in the chiral Lagrangian induce mixing between the bare charmonium fields, necessitating a diagonalization procedure to correctly identify the physical $J/ψ$ and $ψ'$ states. Following this diagonalization, we relate the threshold scattering amplitudes of $J/ψ{\cal P}~({\cal P}=π,K)$, which determine the scattering lengths, to the $J/ψJ/ψ\to {\cal P}\bar{\cal P}$ amplitudes via crossing symmetry. The ${\cal P}\bar{\cal P}$ rescattering effects are incorporated using dispersion relations. We obtain the $S$-wave scattering lengths $a_{J/ψπ} \lesssim -0.0021$~fm and $a_{J/ψK} \lesssim -0.028$~fm, where the negative sign indicates an attractive interaction. Our results show that the $J/ψK$ interaction is moderately enhanced relative to the pion channel, driven by explicit chiral symmetry breaking. Furthermore, a quantitative comparison of the coupled-channel mechanism, where $J/ψπ$ couples to $D\bar{D}^*$ and $J/ψK$ couples to $D^*\bar{D}_s/D\bar{D}_s^*$, reveals that both $J/ψπ$ and $J/ψK$ scatterings are predominantly governed by the soft-gluon exchange mechanism. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_18103 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Scattering lengths of the $J/ψπ$ and $J/ψK$ systems Yan, Jiang Cao, Xiong-Hui Du, Meng-Lin Guo, Feng-Kun High Energy Physics - Phenomenology We investigate the low-energy interactions between the charmonium state $J/ψ$ and the light pseudoscalar mesons ($π$ and $K$) within the framework of dispersion relations.We demonstrate that the symmetry-breaking terms in the chiral Lagrangian induce mixing between the bare charmonium fields, necessitating a diagonalization procedure to correctly identify the physical $J/ψ$ and $ψ'$ states. Following this diagonalization, we relate the threshold scattering amplitudes of $J/ψ{\cal P}~({\cal P}=π,K)$, which determine the scattering lengths, to the $J/ψJ/ψ\to {\cal P}\bar{\cal P}$ amplitudes via crossing symmetry. The ${\cal P}\bar{\cal P}$ rescattering effects are incorporated using dispersion relations. We obtain the $S$-wave scattering lengths $a_{J/ψπ} \lesssim -0.0021$~fm and $a_{J/ψK} \lesssim -0.028$~fm, where the negative sign indicates an attractive interaction. Our results show that the $J/ψK$ interaction is moderately enhanced relative to the pion channel, driven by explicit chiral symmetry breaking. Furthermore, a quantitative comparison of the coupled-channel mechanism, where $J/ψπ$ couples to $D\bar{D}^*$ and $J/ψK$ couples to $D^*\bar{D}_s/D\bar{D}_s^*$, reveals that both $J/ψπ$ and $J/ψK$ scatterings are predominantly governed by the soft-gluon exchange mechanism. |
| title | Scattering lengths of the $J/ψπ$ and $J/ψK$ systems |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2601.18103 |