{
  "id": "1012.4323",
  "version": "v1",
  "published": "2010-12-20T13:36:03.000Z",
  "updated": "2010-12-20T13:36:03.000Z",
  "title": "On the color suppressed contribution to $\\bar{B_{d}^0} \\rightarrow \\, π^0 π^{0}",
  "authors": [
    "Jan O. Eeg",
    "Teresa Palmer"
  ],
  "comment": "The submitted Latex version correspond to 23 pages in ps-version and contains 4 figures",
  "journal": "Phys.Rev.D83:054016,2011",
  "doi": "10.1103/PhysRevD.83.054016",
  "categories": [
    "hep-ph"
  ],
  "abstract": "The decay modes of the type $B \\rightarrow \\pi \\, \\pi $ are dynamically different. For the case $\\bar{B_{d}^0} \\rightarrow \\, \\pi^+ \\pi^- $ there is a substantial factorized contribution which dominates. In contrast, the decay mode $\\bar{B_{d}^0} \\rightarrow \\, \\pi^0 \\pi^{0} $ has a small factorized contribution, being proportional to a small Wilson coefficient combination. However, for the decay mode $\\bar{B_{d}^0} \\rightarrow \\, \\pi^0 \\pi^{0} $ there is a sizeable nonfactorizable (color suppressed) contribution due to soft (long distance) interactions, which dominate the amplitude. We estimate the branching ratio for the mode $\\bar{B_{d}^0} \\rightarrow \\, \\pi^0 \\pi^{0} $ in the heavy quark limit for the $b$- quark. In order to estimate color suppressed contributions we treat the energetic light ($u,d,s$) quark within a variant of Large Energy Effective Theory combined with a recent extension of chiral quark models in terms of model- dependent gluon condensates. We find that our calculated color suppressed amplitude is suppressed by a factor of order $\\Lambda_{QCD}/m_b$ with respect to the factorizable amplitude, as it should according to QCD-factorization. Further, for reasonable values of the constituent quark mass and the gluon condensate, the calculated nonfactorizable amplitude for $\\bar{B_{d}^0} \\rightarrow \\, \\pi^0 \\pi^{0} $ can easily accomodate the experimental value. Unfortunately, the color suppressed amplitude is very sensitive to the values of these model dependent parameters. Therefore fine-tuning is necessary in order to obtain an amplitude compatible with the experimental result for $\\bar{B_{d}^0} \\rightarrow \\, \\pi^0 \\pi^{0} $. A possible link to the triangle anomaly is discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-12-20T13:36:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "13.20.He",
      "12.39.Fe",
      "12.39.St",
      "12.39.Hg"
    ],
    "keywords": [
      "decay mode",
      "color suppressed amplitude",
      "small wilson coefficient combination",
      "factorized contribution",
      "estimate color suppressed contributions"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review D",
      "year": 2011,
      "month": "Mar",
      "volume": 83,
      "number": 5,
      "pages": "054016"
    },
    "note": {
      "typesetting": "LaTeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 882474,
      "adsabs": "2011PhRvD..83e4016E"
    }
  }
}