Solving the left-hand cut problem in lattice QCD: $T_{cc}(3875)^+$ from finite volume energy levels
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
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2023
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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 | We discuss a novel effective-field-theory-based approach for extracting two-body scattering information from finite volume energies, serving as an alternative to Lüscher's method. By explicitly incorporating one-pion exchange, we overcome the challenging left-hand cut problem in Lüscher's method and can handle finite volume energy levels both below and above the left-hand cut. Applied to the lattice data for $DD^*$ scattering at a pion mass of 280 MeV, as an illustrative example, our results reveal the significant impact of the one-pion exchange on P-wave and S-wave phase shifts. The pole position of the $T_{cc}(3875)^+$ state, extracted from the finite-volume energy levels at this pion mass while taking into account left-hand cut effects, range corrections and partial-wave mixing, is consistent with a near-threshold resonance. This study demonstrates, for the first time, that two-body scattering information can be reliably extracted from lattice spectra including the left-hand cut. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_01930 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Solving the left-hand cut problem in lattice QCD: $T_{cc}(3875)^+$ from finite volume energy levels Meng, Lu Baru, Vadim Epelbaum, Evgeny Filin, Arseniy A. Gasparyan, Ashot M. High Energy Physics - Lattice High Energy Physics - Phenomenology Nuclear Theory We discuss a novel effective-field-theory-based approach for extracting two-body scattering information from finite volume energies, serving as an alternative to Lüscher's method. By explicitly incorporating one-pion exchange, we overcome the challenging left-hand cut problem in Lüscher's method and can handle finite volume energy levels both below and above the left-hand cut. Applied to the lattice data for $DD^*$ scattering at a pion mass of 280 MeV, as an illustrative example, our results reveal the significant impact of the one-pion exchange on P-wave and S-wave phase shifts. The pole position of the $T_{cc}(3875)^+$ state, extracted from the finite-volume energy levels at this pion mass while taking into account left-hand cut effects, range corrections and partial-wave mixing, is consistent with a near-threshold resonance. This study demonstrates, for the first time, that two-body scattering information can be reliably extracted from lattice spectra including the left-hand cut. |
| title | Solving the left-hand cut problem in lattice QCD: $T_{cc}(3875)^+$ from finite volume energy levels |
| topic | High Energy Physics - Lattice High Energy Physics - Phenomenology Nuclear Theory |
| url | https://arxiv.org/abs/2312.01930 |