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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/2505.02878 |
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| _version_ | 1866918009708216320 |
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| author | Yamada, Wren Morimatsu, Osamu Sato, Toru Yazaki, Koichi |
| author_facet | Yamada, Wren Morimatsu, Osamu Sato, Toru Yazaki, Koichi |
| contents | We analyze the pole expansion of the two-hadron imaginary-time correlation function. We first explain the general idea that the imaginary-time correlation function is expressed as a sum of the pole terms, the Mittag-Leffler expansion, in terms of the uniformization variable, which makes the S-matrix single-valued. We then derive explicit expressions of the pole expansion for the single-channel ($ρ$ meson) and two-channel ($Λ(1405)$) examples and demonstrate that the pole expansion actually holds employing phenomenological models, the vector-dominance model for the $ρ$ meson and the chiral unitary model for $Λ(1405)$. From this observation we propose the pole expansion as a method to extract information of unstable states such as masses and widths from the two-hadron imaginary-time correlation functions obtained by lattice QCD simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_02878 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pole-Expansion of Two-Hadron Imaginary-Time Correlation Function -a new method of analysis for unstable states in lattice QCD- Yamada, Wren Morimatsu, Osamu Sato, Toru Yazaki, Koichi High Energy Physics - Lattice Nuclear Theory We analyze the pole expansion of the two-hadron imaginary-time correlation function. We first explain the general idea that the imaginary-time correlation function is expressed as a sum of the pole terms, the Mittag-Leffler expansion, in terms of the uniformization variable, which makes the S-matrix single-valued. We then derive explicit expressions of the pole expansion for the single-channel ($ρ$ meson) and two-channel ($Λ(1405)$) examples and demonstrate that the pole expansion actually holds employing phenomenological models, the vector-dominance model for the $ρ$ meson and the chiral unitary model for $Λ(1405)$. From this observation we propose the pole expansion as a method to extract information of unstable states such as masses and widths from the two-hadron imaginary-time correlation functions obtained by lattice QCD simulations. |
| title | Pole-Expansion of Two-Hadron Imaginary-Time Correlation Function -a new method of analysis for unstable states in lattice QCD- |
| topic | High Energy Physics - Lattice Nuclear Theory |
| url | https://arxiv.org/abs/2505.02878 |