Left-hand cut problem in lattice QCD and an EFT-based solution
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913768334688256 |
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| author | Meng, Lu Baru, Vadim Epelbaum, Evgeny Filin, Arseniy A. Gasparyan, Ashot M. |
| author_facet | Meng, Lu Baru, Vadim Epelbaum, Evgeny Filin, Arseniy A. Gasparyan, Ashot M. |
| contents | Lattice QCD has become an essential tool for studying the hadron-hadron interaction from the first principles. However, when extracting infinite-volume scattering parameters from finite-volume energy levels, the traditional Lüscher formula encounters limitations due to the left-hand cut induced by long-range interactions such as the one-pion exchange. In this work, we propose an alternative approach based on chiral effective field theory combined with a Hamiltonian method in the plane wave basis. By solving a Schrödinger-like equation in the finite volume, our method connects the finite-volume energy spectrum with infinite-volume observables, while systematically incorporating the long-range physics and solving the left-hand cut problem. The use of the plane wave basis mitigates issues related to partial wave mixing. Our numerical results for $DD^*$ scattering at $m_π\approx$ 280 MeV demonstrate that this approach overcomes the limitations of the Lüscher method and points towards a resonance interpretation of the $T_{cc}(3875)$ state, as opposed to the virtual state predicted by traditional analyses. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_23944 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Left-hand cut problem in lattice QCD and an EFT-based solution Meng, Lu Baru, Vadim Epelbaum, Evgeny Filin, Arseniy A. Gasparyan, Ashot M. High Energy Physics - Lattice Lattice QCD has become an essential tool for studying the hadron-hadron interaction from the first principles. However, when extracting infinite-volume scattering parameters from finite-volume energy levels, the traditional Lüscher formula encounters limitations due to the left-hand cut induced by long-range interactions such as the one-pion exchange. In this work, we propose an alternative approach based on chiral effective field theory combined with a Hamiltonian method in the plane wave basis. By solving a Schrödinger-like equation in the finite volume, our method connects the finite-volume energy spectrum with infinite-volume observables, while systematically incorporating the long-range physics and solving the left-hand cut problem. The use of the plane wave basis mitigates issues related to partial wave mixing. Our numerical results for $DD^*$ scattering at $m_π\approx$ 280 MeV demonstrate that this approach overcomes the limitations of the Lüscher method and points towards a resonance interpretation of the $T_{cc}(3875)$ state, as opposed to the virtual state predicted by traditional analyses. |
| title | Left-hand cut problem in lattice QCD and an EFT-based solution |
| topic | High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2503.23944 |