{
  "id": "1511.00031",
  "version": "v1",
  "published": "2015-10-30T21:11:35.000Z",
  "updated": "2015-10-30T21:11:35.000Z",
  "title": "Large-$N$ pion scattering at finite temperature: the $f_0(500)$ and chiral restoration",
  "authors": [
    "Santiago Cortes",
    "Angel Gomez Nicola",
    "John Morales"
  ],
  "comment": "24 pages, 12 figures",
  "categories": [
    "hep-ph"
  ],
  "abstract": "We consider the $O(N+1)/O(N)$ Non-Linear Sigma Model for large $N$ as an effective theory for low-energy QCD at finite temperature $T$, in the chiral limit. At $T=0$ this formulation provides a good description of scattering data in the scalar channel and generates dynamically the $f_0(500)$ pole, the pole position lying within experimental determinations. Previous $T=0$ results with this model are updated using newer analysis of pion scattering data. We calculate the pion scattering amplitude at finite $T$ and show that it satisfies exactly thermal unitarity, which had been assumed but not formally proven in previous works. We discuss the main differences with the $T=0$ result and we show that one can define a proper renormalization scheme with $T=0$ counterterms such that the renormalized amplitude can be chosen to depend only on a few parameters. Next, we analyze the behaviour of the $f_0(500)$ pole at finite $T$, which is consistent with chiral symmetry restoration when the scalar susceptibility is saturated by the $f_0(500)$ state, in a second-order transition scenario and in accordance with lattice and theoretical analysis.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-30T21:11:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite temperature",
      "chiral restoration",
      "non-linear sigma model",
      "second-order transition scenario",
      "satisfies exactly thermal unitarity"
    ],
    "publication": {
      "doi": "10.1103/PhysRevD.93.036001"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1402372
    }
  }
}