dorsal/arxiv
View SchemaThe Three-Boson System with Short-Range Interactions
| Authors | P. F. Bedaque, H. -W. Hammer, U. van Kolck |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/9811046 |
| URL | https://arxiv.org/abs/nucl-th/9811046 |
| DOI | 10.1016/S0375-9474(98)00650-2 |
| Journal | Nucl.Phys. A646 (1999) 444-466 |
Abstract
We discuss renormalization of the non-relativistic three-body problem with short-range forces. The problem is non-perturbative at momenta of the order of the inverse of the two-body scattering length. An infinite number of graphs must be summed, which leads to a cutoff dependence that does not appear in any order in perturbation theory. We argue that this cutoff dependence can be absorbed in one local three-body force counterterm and compute the running of the three-body force with the cutoff. This allows a calculation of the scattering of a particle and the two-particle bound state if the corresponding scattering length is used as input. We also obtain a model-independent relation between binding energy of a shallow three-body bound state and this scattering length. We comment on the power counting that organizes higher-order corrections and on relevance of this result for the effective field theory program in nuclear and molecular physics.
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"abstract": "We discuss renormalization of the non-relativistic three-body problem with\nshort-range forces. The problem is non-perturbative at momenta of the order of\nthe inverse of the two-body scattering length. An infinite number of graphs\nmust be summed, which leads to a cutoff dependence that does not appear in any\norder in perturbation theory. We argue that this cutoff dependence can be\nabsorbed in one local three-body force counterterm and compute the running of\nthe three-body force with the cutoff. This allows a calculation of the\nscattering of a particle and the two-particle bound state if the corresponding\nscattering length is used as input. We also obtain a model-independent relation\nbetween binding energy of a shallow three-body bound state and this scattering\nlength. We comment on the power counting that organizes higher-order\ncorrections and on relevance of this result for the effective field theory\nprogram in nuclear and molecular physics.",
"arxiv_id": "nucl-th/9811046",
"authors": [
"P. F. Bedaque",
"H. -W. Hammer",
"U. van Kolck"
],
"categories": [
"nucl-th",
"hep-ph",
"physics.atm-clus"
],
"doi": "10.1016/S0375-9474(98)00650-2",
"journal_ref": "Nucl.Phys. A646 (1999) 444-466",
"title": "The Three-Boson System with Short-Range Interactions",
"url": "https://arxiv.org/abs/nucl-th/9811046"
},
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