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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2504.01545 |
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| _version_ | 1866916671630868480 |
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| author | Meng, Lu |
| author_facet | Meng, Lu |
| contents | Lattice QCD has become a crucial tool for studying hadron-hadron interactions from first principles. However, significant challenges arise when extracting infinite-volume scattering parameters from finite-volume energy levels using the conventional Lüscher method, particularly due to the presence of left-hand cuts induced by long-range interactions such as the one-pion exchange. To address these limitations, we propose a novel framework that combines chiral effective field theory and the plane-wave expansion with the Hamiltonian approach. By solving a Schrödinger-like equation in a finite volume, this method establishes a connection between finite-volume energy spectra and infinite-volume physical quantities, while effectively handling issues caused by left-hand cuts. Furthermore, the adoption of a plane-wave basis helps mitigating complexities associated with partial-wave mixing. Our preliminary numerical results at $m_π\approx 280$ MeV confirm that this approach efficiently overcomes the shortcomings of the Lüscher method and indicate a resonant interpretation of the $T_{cc}(3875)$ state--in contrast to the virtual state suggested in conventional analyses. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_01545 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $T_{cc}$ from finite volume energy levels: the left-hand cut problem and its solution Meng, Lu High Energy Physics - Lattice Lattice QCD has become a crucial tool for studying hadron-hadron interactions from first principles. However, significant challenges arise when extracting infinite-volume scattering parameters from finite-volume energy levels using the conventional Lüscher method, particularly due to the presence of left-hand cuts induced by long-range interactions such as the one-pion exchange. To address these limitations, we propose a novel framework that combines chiral effective field theory and the plane-wave expansion with the Hamiltonian approach. By solving a Schrödinger-like equation in a finite volume, this method establishes a connection between finite-volume energy spectra and infinite-volume physical quantities, while effectively handling issues caused by left-hand cuts. Furthermore, the adoption of a plane-wave basis helps mitigating complexities associated with partial-wave mixing. Our preliminary numerical results at $m_π\approx 280$ MeV confirm that this approach efficiently overcomes the shortcomings of the Lüscher method and indicate a resonant interpretation of the $T_{cc}(3875)$ state--in contrast to the virtual state suggested in conventional analyses. |
| title | $T_{cc}$ from finite volume energy levels: the left-hand cut problem and its solution |
| topic | High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2504.01545 |