{
  "id": "1510.00118",
  "version": "v1",
  "published": "2015-10-01T06:27:33.000Z",
  "updated": "2015-10-01T06:27:33.000Z",
  "title": "The Coulomb interaction in Helium-3: Interplay of strong short-range and weak long-range potentials",
  "authors": [
    "J. Kirscher",
    "D. Gazit"
  ],
  "comment": "submitted version; 4 figures",
  "categories": [
    "nucl-th"
  ],
  "abstract": "Quantum chromodynamics and the electroweak theory at low energies are prominent instances of the combination of a short-range and a long-range interaction. For the description of light nuclei, the large nucleon-nucleon scattering lengths produced by the strong interaction, and the reduction of the weak interaction to the Coulomb potential, play a crucial role. Helium-3 is the first bound nucleus comprised of more than one proton in which this combination of forces can be studied. We demonstrate a proper renormalization of Helium-3 using the pionless effective field theory as the formal representation of the nuclear regime as strongly interacting fermions. The theory is found consistent at leading and next-to-leading order without isospin-symmetry-breaking 3-nucleon interactions and a non-perturbative treatment of the Coulomb interaction. The conclusion highlights the significance of the regularization method since a comparison to previous work is contradictory if the difference in those methods is not considered. With a perturbative Coulomb interaction, as suggested by dimensional analysis, we find the Helium-3 system properly renormalized, too. For both treatments, renormalization-scheme independence of the effective field theory is demonstrated by regulating the potential and a variation of the associated cutoff.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-01T06:27:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "coulomb interaction",
      "weak long-range potentials",
      "strong short-range",
      "effective field theory",
      "large nucleon-nucleon scattering lengths"
    ],
    "publication": {
      "doi": "10.1016/j.physletb.2016.02.011"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1395653
    }
  }
}