{
  "id": "0708.3526",
  "version": "v3",
  "published": "2007-08-27T02:20:50.000Z",
  "updated": "2007-11-17T06:34:04.000Z",
  "title": "1/N_c corrections to the magnetic susceptibility of the QCD vacuum",
  "authors": [
    "Klaus Goeke",
    "Hyun-Chul Kim",
    "M. M. Musakhanov",
    "Marat Siddikov"
  ],
  "comment": "18 pages, 5 figures. Final version to appear in Phys. Rev. D",
  "journal": "Phys.Rev.D76:116007,2007",
  "doi": "10.1103/PhysRevD.76.116007",
  "categories": [
    "hep-ph"
  ],
  "abstract": "We investigate the magnetic susceptibility of the QCD vacuum with the $1/N_c$ corrections taken into account, based on the instanton vacuum. Starting from the instanton liquid model we derive the gauged light-quark partition function in the presence of the current quark mass as well as of external Abelian vector and tensor fields. We consider the $1/N_c$ meson-loop corrections which are shown to contribute to the magnetic susceptibility by around 15% for the up (and down) quarks. We also take into account the tensor terms of the quark-quark interaction from the instanton vacuum as well as the finite-width effects, both of which are of order $\\mathcal{O}(1/N_c)$. The effects of the tensor terms and finite width turn out to be negligibly small. The final results for the up-quarks are given as: $\\chi< i\\psi^\\dagger \\psi>_0 \\simeq 35-40 \\mathrm{MeV}$ with the quark condensate $<i\\psi^\\dagger \\psi>_0$. We also discuss the pion mass dependence of the magnetic susceptibility in order to give a qualitative guideline for the chiral extrapolation of lattice data.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2007-11-17T06:34:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11.15.Pg",
      "11.15.Kc",
      "11.10.Lm",
      "11.30.Rd"
    ],
    "keywords": [
      "magnetic susceptibility",
      "qcd vacuum",
      "instanton vacuum",
      "tensor terms",
      "instanton liquid model"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review D",
      "year": 2007,
      "month": "Dec",
      "volume": 76,
      "number": 11,
      "pages": 116007
    },
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 759151,
      "adsabs": "2007PhRvD..76k6007G"
    }
  }
}