$T_{cc}^+$ and $X(3872)$ with the complex scaling method and $DD(\bar{D})π$ three-body effect
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866912117046640640 |
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| author | Lin, Zi-Yang Cheng, Jian-Bo Zhu, Shi-Lin |
| author_facet | Lin, Zi-Yang Cheng, Jian-Bo Zhu, Shi-Lin |
| contents | We use the leading order (LO) contact interactions and OPE potentials to investigate the newly observed double-charm state $T_{cc}^+$. The $DDπ$ three-body effect is important in this system since the intermediate states can go on shell. We keep the dependence of the pion propagators on the center-of-mass energy, which results in a unitary cut of the OPE potential at the $DDπ$ three-body threshold. By solving the complex scaled Schrödinger equation, we find a pole corresponding to the $T_{cc}^+$ on the physical Riemann sheet. Its width is around 80 keV and nearly independent of the choice of the cutoff. Assuming the $D\bar{D}π$ and $D\bar{D}^*$ channels as the main decay channels, we apply the similar calculations to the $X(3872)$, and find its width is even smaller. Besides, the isospin breaking effect is significant for the $X(3872)$ while its impact on the $T_{cc}^+$ is relatively small. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_14628 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | $T_{cc}^+$ and $X(3872)$ with the complex scaling method and $DD(\bar{D})π$ three-body effect Lin, Zi-Yang Cheng, Jian-Bo Zhu, Shi-Lin High Energy Physics - Phenomenology We use the leading order (LO) contact interactions and OPE potentials to investigate the newly observed double-charm state $T_{cc}^+$. The $DDπ$ three-body effect is important in this system since the intermediate states can go on shell. We keep the dependence of the pion propagators on the center-of-mass energy, which results in a unitary cut of the OPE potential at the $DDπ$ three-body threshold. By solving the complex scaled Schrödinger equation, we find a pole corresponding to the $T_{cc}^+$ on the physical Riemann sheet. Its width is around 80 keV and nearly independent of the choice of the cutoff. Assuming the $D\bar{D}π$ and $D\bar{D}^*$ channels as the main decay channels, we apply the similar calculations to the $X(3872)$, and find its width is even smaller. Besides, the isospin breaking effect is significant for the $X(3872)$ while its impact on the $T_{cc}^+$ is relatively small. |
| title | $T_{cc}^+$ and $X(3872)$ with the complex scaling method and $DD(\bar{D})π$ three-body effect |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2205.14628 |