Two-body double pole and three-body bound states: physical and unphysical quark masses
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866914640722657280 |
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| author | Timoteo, V. S. van Kolck, U. |
| author_facet | Timoteo, V. S. van Kolck, U. |
| contents | We solve the Faddeev bound-state equations for three particles with simple two-body nonlocal, separable potentials that yield a scattering length twice as large as a positive effective range, as indicated by some lattice QCD simulations. Neglecting shape parameters, the two-body bound state is a double pole. For bosons we obtain a correlation between three- and two-body energies. For nucleons, this correlation depends additionally on the ratio of effective ranges in the two two-body $S$-wave channels. When this ratio takes the value suggested by lattice QCD, our three-body energy agrees well with a direct lattice determination. When this ratio takes the experimental value, we find a three-body bound state with energy close to that of the physical triton. We suggest that results could be improved systematically with distorted-wave perturbation theory around a separable potential whose form factor is an inverse square root of momentum squared. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_01165 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Two-body double pole and three-body bound states: physical and unphysical quark masses Timoteo, V. S. van Kolck, U. Nuclear Theory We solve the Faddeev bound-state equations for three particles with simple two-body nonlocal, separable potentials that yield a scattering length twice as large as a positive effective range, as indicated by some lattice QCD simulations. Neglecting shape parameters, the two-body bound state is a double pole. For bosons we obtain a correlation between three- and two-body energies. For nucleons, this correlation depends additionally on the ratio of effective ranges in the two two-body $S$-wave channels. When this ratio takes the value suggested by lattice QCD, our three-body energy agrees well with a direct lattice determination. When this ratio takes the experimental value, we find a three-body bound state with energy close to that of the physical triton. We suggest that results could be improved systematically with distorted-wave perturbation theory around a separable potential whose form factor is an inverse square root of momentum squared. |
| title | Two-body double pole and three-body bound states: physical and unphysical quark masses |
| topic | Nuclear Theory |
| url | https://arxiv.org/abs/2304.01165 |