{
  "id": "2411.00386",
  "version": "v1",
  "published": "2024-11-01T06:16:22.000Z",
  "updated": "2024-11-01T06:16:22.000Z",
  "title": "Scale-(in)dependence in quantum 4-body scattering",
  "authors": [
    "Sourav Mondal",
    "Rakshanda Goswami",
    "Udit Raha",
    "Johannes Kirscher"
  ],
  "comment": "15 pages, 4 figures, 2 tables",
  "categories": [
    "nucl-th",
    "cond-mat.quant-gas",
    "physics.atom-ph"
  ],
  "abstract": "We investigate the multi-channel 4-body scattering system using regularized 2- and 3-body contact interactions. The analysis determines the sensitivity of bound-state energies, scattering phase shifts and cross sections on the cutoff parameter ($\\lambda$), and the energy gaps between scattering thresholds. The latter dependency is obtained with a 2-body scale fixed to an unnaturally large value and a floating 3-body parameter. Specifically, we calculate the binding energies of the shallow 3- and 4-body states, dimer-dimer and trimer-atom scattering lengths, and the trimer-atom to dimer-dimer reaction rates. Employing a potential renormalized by a large 2-body scattering length and a 3-body scale, we find all calculated observables to remain practically constant over the range $6\\textrm{fm}^{-2}<\\lambda<10\\textrm{fm}^{-2}$. Divergences in scattering lengths emerge for critical 3-body parameters at which thresholds are degenerate. Such threshold effects are found to be independent of the regulator cutoff. Furthermore, at those critical points where the dimer-dimer and trimer-atom thresholds overlap, we predict an enhancement of the inelastic over the elastic scattering event. Such an inversion between elastic- and rearrangement-collision probabilities indicates a strong sensitivity of the 4-body reaction dynamics on the 3-body parameter at finite 2-body scale. This phenomenon is absent in earlier studies which differ in the renormalization scheme. As this discrepancy arises for all considered cutoffs, a more comprehensive parametrization of short-distance structure is necessary: sole cutoff variation does not reveal non-perturbative change in reaction rates conjectured to be due to a combined effect of the finite 2-body range and the specific choice for the 3-body parameter.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-11-01T06:16:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "scattering length",
      "dependence",
      "trimer-atom thresholds overlap",
      "dimer-dimer reaction rates",
      "sole cutoff variation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}