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Main Authors: Yu, Kang, Wang, Guang-Juan, Wu, Jia-Jun, Yang, Zhi
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2502.05789
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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