dorsal/arxiv
View SchemaPrecise numerical results for limit cycles in the quantum three-body problem
| Authors | R. F. Mohr, R. J. Furnstahl, H. -W. Hammer, R. J. Perry, K. G. Wilson |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/0509076 |
| URL | https://arxiv.org/abs/nucl-th/0509076 |
| DOI | 10.1016/j.aop.2005.10.002 |
| Journal | Annals Phys. 321 (2006) 225-259 |
Abstract
The study of the three-body problem with short-range attractive two-body forces has a rich history going back to the 1930's. Recent applications of effective field theory methods to atomic and nuclear physics have produced a much improved understanding of this problem, and we elucidate some of the issues using renormalization group ideas applied to precise nonperturbative calculations. These calculations provide 11-12 digits of precision for the binding energies in the infinite cutoff limit. The method starts with this limit as an approximation to an effective theory and allows cutoff dependence to be systematically computed as an expansion in powers of inverse cutoffs and logarithms of the cutoff. Renormalization of three-body bound states requires a short range three-body interaction, with a coupling that is governed by a precisely mapped limit cycle of the renormalization group. Additional three-body irrelevant interactions must be determined to control subleading dependence on the cutoff and this control is essential for an effective field theory since the continuum limit is not likely to match physical systems ({\it e.g.}, few-nucleon bound and scattering states at low energy). Leading order calculations precise to 11-12 digits allow clear identification of subleading corrections, but these corrections have not been computed.
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"abstract": "The study of the three-body problem with short-range attractive two-body\nforces has a rich history going back to the 1930\u0027s. Recent applications of\neffective field theory methods to atomic and nuclear physics have produced a\nmuch improved understanding of this problem, and we elucidate some of the\nissues using renormalization group ideas applied to precise nonperturbative\ncalculations. These calculations provide 11-12 digits of precision for the\nbinding energies in the infinite cutoff limit. The method starts with this\nlimit as an approximation to an effective theory and allows cutoff dependence\nto be systematically computed as an expansion in powers of inverse cutoffs and\nlogarithms of the cutoff. Renormalization of three-body bound states requires a\nshort range three-body interaction, with a coupling that is governed by a\nprecisely mapped limit cycle of the renormalization group. Additional\nthree-body irrelevant interactions must be determined to control subleading\ndependence on the cutoff and this control is essential for an effective field\ntheory since the continuum limit is not likely to match physical systems ({\\it\ne.g.}, few-nucleon bound and scattering states at low energy). Leading order\ncalculations precise to 11-12 digits allow clear identification of subleading\ncorrections, but these corrections have not been computed.",
"arxiv_id": "nucl-th/0509076",
"authors": [
"R. F. Mohr",
"R. J. Furnstahl",
"H. -W. Hammer",
"R. J. Perry",
"K. G. Wilson"
],
"categories": [
"nucl-th",
"hep-ph",
"physics.atom-ph"
],
"doi": "10.1016/j.aop.2005.10.002",
"journal_ref": "Annals Phys. 321 (2006) 225-259",
"title": "Precise numerical results for limit cycles in the quantum three-body problem",
"url": "https://arxiv.org/abs/nucl-th/0509076"
},
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