{
  "annotation_id": "33f8b9cf-305d-4aba-96fb-40929af9366c",
  "date_created": "2026-03-02T18:00:11.278000Z",
  "date_modified": "2026-03-02T18:00:11.278000Z",
  "file_hash": "39c4b78144de87b4cd4d1376ca577bcd7bf648c0a3c5a34cec231a3811fff127",
  "private": false,
  "record": {
    "abstract": "A modified Low procedure for constructing soft-photon amplitudes has been\nused to derive two general soft-photon amplitudes, a two-s-two-t special\namplitude $M^{TsTts}_{\\mu}$ and a two-u-two-t special amplitude\n$M^{TuTts}_{\\mu}$, where s, t and u are the Mandelstam variables.\n$M^{TsTts}_{\\mu}$ depends only on the elastic T-matrix evaluated at four sets\nof (s,t) fixed by the requirement that the amplitude be free of derivatives\n($\\partial$T/$\\partial$s and /or $\\partial$T/$\\partial t$). Likewise\n$M^{TuTts}_{\\mu}$ depends only on the elastic T-matrix evaluated at four sets\nof (u,t). In deriving these amplitudes, we impose the condition that\n$M^{TsTts}_{\\mu}$ and $M^{TuTts}_{\\mu}$ reduce to $\\bar{M}^{TsTts}_{\\mu}$ and\n$\\bar{M}^{TuTts}_{\\mu}$, respectively, their tree level approximations. The\namplitude $\\bar{M}^{TsTts}_{\\mu}$ represents photon emission from a sum of\none-particle t-channel exchange diagrams and one-particle s-channel exchange\ndiagrams, while the amplitude $\\bar{M}^{TuTts} _{\\mu}$ represents photon\nemission from a sum of one-particle t-channel exchange diagrams and\none-particle u-channel exchange diagrams. The precise expressions for\n$\\bar{M}^{TsTts}_{\\mu}$ and $\\bar{M}^{TuTts}_{\\mu}$ are determined by using the\nradiation decomposition identities of Brodsky and Brown. We point out that it\nis theoretically impossible to describe all bremsstrahlung processes by using\nonly a single class of soft-photon amplitudes. At least two different classes\nare required: the amplitudes which depend on s and t or the amplitudes which\ndepend on u and t. When resonance effects are important, the amplitude\n$M^{TsTts}_{\\mu}$, not $M^{Low(st)}_{\\mu}$, should be used. For processes with\nstrong u-channel exchange effects, the amplitude $M^{TuTts}_{\\mu}$ should be\nthe first choice.",
    "arxiv_id": "nucl-th/9210006",
    "authors": [
      "M. K. Liou",
      "Dahang Lin",
      "B. F. Gibson"
    ],
    "categories": [
      "nucl-th"
    ],
    "doi": "10.1103/PhysRevC.47.973",
    "title": "Anatomy of the Soft-Photon Approximation in Hadron-Hadron Bremsstrahlung",
    "url": "https://arxiv.org/abs/nucl-th/9210006"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "3383c493-c039-413c-a472-0f16ec3c328f",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}