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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.05789 |
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| _version_ | 1866908718940028928 |
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| author | Yu, Kang Wang, Guang-Juan Wu, Jia-Jun Yang, Zhi |
| author_facet | Yu, Kang Wang, Guang-Juan Wu, Jia-Jun Yang, Zhi |
| contents | We propose a systematic method to block-diagonalize the finite volume effective Hamiltonian for two-particle systems with arbitrary spin in both the rest and moving frame. The framework is convenient and efficient for addressing the left-hand cut issue arising from long-range potential, which are challenging in the framework of standard Lüscher formula. Furthermore, the method provides a foundation for further extension to three-particle systems. We first benchmark our method by examining several toy models, demonstrating its consistency with standard Lüscher formula in the absence of long-range potential. In the presence of long-range potential, we investigate and resolve the effects and issues of left-hand cut. As a realistic application, we calculate the finite volume spectra of isoscalar $D\bar{D}^*$ system, where the well-known exotic state $χ_{c1}(3872)$ is observed. The results are qualitatively consistent with the lattice QCD calculation, highlighting the reliability and potential application of our framework to the study of other exotic states in hadron physics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_05789 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Finite Volume Hamiltonian method for two-particle systems containing long-range potential on the lattice Yu, Kang Wang, Guang-Juan Wu, Jia-Jun Yang, Zhi High Energy Physics - Lattice We propose a systematic method to block-diagonalize the finite volume effective Hamiltonian for two-particle systems with arbitrary spin in both the rest and moving frame. The framework is convenient and efficient for addressing the left-hand cut issue arising from long-range potential, which are challenging in the framework of standard Lüscher formula. Furthermore, the method provides a foundation for further extension to three-particle systems. We first benchmark our method by examining several toy models, demonstrating its consistency with standard Lüscher formula in the absence of long-range potential. In the presence of long-range potential, we investigate and resolve the effects and issues of left-hand cut. As a realistic application, we calculate the finite volume spectra of isoscalar $D\bar{D}^*$ system, where the well-known exotic state $χ_{c1}(3872)$ is observed. The results are qualitatively consistent with the lattice QCD calculation, highlighting the reliability and potential application of our framework to the study of other exotic states in hadron physics. |
| title | Finite Volume Hamiltonian method for two-particle systems containing long-range potential on the lattice |
| topic | High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2502.05789 |