{
  "id": "nucl-th/0502039",
  "version": "v2",
  "published": "2005-02-14T17:01:30.000Z",
  "updated": "2005-07-04T10:30:28.000Z",
  "title": "Naive Dimensional Analysis for Three-Body Forces Without Pions",
  "authors": [
    "Harald W. Griesshammer"
  ],
  "comment": "31 pages LaTeX2e, including 8 figures in 13 .eps files, embedded with includegraphicx; linguistic corrections only, version to appear in Nucl Phys A",
  "journal": "Nucl.Phys. A760 (2005) 110-138",
  "doi": "10.1016/j.nuclphysa.2005.05.202",
  "categories": [
    "nucl-th",
    "cond-mat.other",
    "hep-ph",
    "physics.atm-clus"
  ],
  "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.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-07-04T10:30:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "13.75.Cs",
      "27.10.+h",
      "02.30.Uu",
      "25.40.Dn",
      "14.20.Dh",
      "02.30.Rz",
      "21.30.-x",
      "11.80.Jy"
    ],
    "keywords": [
      "three-body force",
      "naive dimensional analysis",
      "short-range forces produce shallow two-particle",
      "produce shallow two-particle bound states",
      "forces produce shallow two-particle bound"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier",
      "journal": "Nucl. Phys. A"
    },
    "note": {
      "typesetting": "LaTeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 676733
    }
  }
}