{
  "id": "1201.4331",
  "version": "v1",
  "published": "2012-01-20T16:25:05.000Z",
  "updated": "2012-01-20T16:25:05.000Z",
  "title": "Pion production in nucleon-nucleon collisions in chiral effective field theory: next-to-next-to-leading order contributions",
  "authors": [
    "A. A. Filin",
    "V. Baru",
    "E. Epelbaum",
    "C. Hanhart",
    "H. Krebs",
    "A. E. Kudryavtsev",
    "F. Myhrer"
  ],
  "comment": "28 pages, 7 figures, 2 tables",
  "doi": "10.1103/PhysRevC.85.054001",
  "categories": [
    "nucl-th"
  ],
  "abstract": "A complete calculation of the pion-nucleon loops that contribute to the transition operator for $NN\\to NN\\pi$ up-to-and-including next-to-next-to-leading order (N$^2$LO) in chiral effective field theory near threshold is presented. The evaluation is based on the so-called momentum counting scheme, which takes into account the relatively large momentum of the initial nucleons inherent in pion-production reactions. We show that the significant cancellations between the loops found at next-to-leading order (NLO) in the earlier studies are also operative at N$^2$LO. In particular, the $1/m_N$ corrections (with $m_N$ being the nucleon mass) to loop diagrams cancel at N$^2$LO, as do the contributions of the pion loops involving the low-energy constants $c_i$, i=1...4. In contrast to the NLO calculation however, the cancellation of loops at N$^2$LO is incomplete, yielding a non-vanishing contribution to the transition amplitude. Together with the one-pion exchange tree-level operators, the loop contributions provide the long-range part of the production operator. Finally, we discuss the phenomenological implications of these findings. In particular, we find that the amplitudes generated by the N$^2$LO pion loops yield contributions comparable in size with the most important phenomenological heavy-meson exchange amplitudes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-01-20T16:25:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "13.75.Cs",
      "13.75.Gx",
      "25.10.+s",
      "12.39.Fe"
    ],
    "keywords": [
      "chiral effective field theory",
      "next-to-next-to-leading order contributions",
      "nucleon-nucleon collisions",
      "pion production",
      "pion loops yield contributions"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review C",
      "year": 2012,
      "month": "May",
      "volume": 85,
      "number": 5,
      "pages": "054001"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1085360,
      "adsabs": "2012PhRvC..85e4001F"
    }
  }
}