dorsal/arxiv
View SchemaNaive Dimensional Analysis for Three-Body Forces Without Pions
| Authors | Harald W. Griesshammer |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/0502039 |
| URL | https://arxiv.org/abs/nucl-th/0502039 |
| DOI | 10.1016/j.nuclphysa.2005.05.202 |
| Journal | Nucl.Phys. A760 (2005) 110-138 |
Abstract
For systems of three identical particles in which short-range forces produce shallow two-particle bound states, and in particular for the ``pion-less'' Effective Field Theory of Nuclear Physics, I extend and systematise the power-counting of three-body forces to all partial-waves and orders, including external currents. With low-energy observables independent of the details of short-distance dynamics, the typical strength of a three-body force is determined from the superficial degree of divergence of the three-body diagrams which contain only two-body forces. This na\"ive dimensional analysis must be amended as the asymptotic solution to the leading-order Faddeev equation depends for large off-shell momenta crucially on the partial wave and spin-combination of the system. It is shown by analytic construction to be weaker in most channels with angular momentum smaller than 3 than expected. This demotes many three-nucleon forces to high orders. Observables like the quartet-S-scattering length are less sensitive to three-nucleon forces than guessed. I also comment on the Efimov effect and limit-cycle for non-zero angular momentum.
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"abstract": "For systems of three identical particles in which short-range forces produce\nshallow two-particle bound states, and in particular for the ``pion-less\u0027\u0027\nEffective Field Theory of Nuclear Physics, I extend and systematise the\npower-counting of three-body forces to all partial-waves and orders, including\nexternal currents. With low-energy observables independent of the details of\nshort-distance dynamics, the typical strength of a three-body force is\ndetermined from the superficial degree of divergence of the three-body diagrams\nwhich contain only two-body forces. This na\\\"ive dimensional analysis must be\namended as the asymptotic solution to the leading-order Faddeev equation\ndepends for large off-shell momenta crucially on the partial wave and\nspin-combination of the system. It is shown by analytic construction to be\nweaker in most channels with angular momentum smaller than 3 than expected.\nThis demotes many three-nucleon forces to high orders. Observables like the\nquartet-S-scattering length are less sensitive to three-nucleon forces than\nguessed. I also comment on the Efimov effect and limit-cycle for non-zero\nangular momentum.",
"arxiv_id": "nucl-th/0502039",
"authors": [
"Harald W. Griesshammer"
],
"categories": [
"nucl-th",
"cond-mat.other",
"hep-ph",
"physics.atm-clus"
],
"doi": "10.1016/j.nuclphysa.2005.05.202",
"journal_ref": "Nucl.Phys. A760 (2005) 110-138",
"title": "Naive Dimensional Analysis for Three-Body Forces Without Pions",
"url": "https://arxiv.org/abs/nucl-th/0502039"
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