{
  "id": "hep-ph/0303070",
  "version": "v4",
  "published": "2003-03-10T03:17:43.000Z",
  "updated": "2003-06-17T08:19:25.000Z",
  "title": "Constraints on the CKM angle $α$ from the measured CP asymmetries and branching ratios of $B \\to π^+ π^-, π^+ π^0$ and $K^0π^+$ decays",
  "authors": [
    "Zhenjun Xiao",
    "Cai-Dian Lü",
    "Libo Guo"
  ],
  "comment": "31 pages, Revtex, 10 PS/EPs figures, some corrections have been made, several new references added. Repot-no: BIHEP-TH-2003-7",
  "categories": [
    "hep-ph",
    "hep-ex"
  ],
  "abstract": "In this paper, we draw constraints on the Cabibbo-Kobayashi-Maskawa (CKM) angle $\\alpha$ and the strong phase $\\delta$ from the experimental measurements of $\\ssb$, the CP-violating asymmetries and branching ratios of $B \\to \\pi^+ \\pi^-, \\pi^+ \\pi^0$ and $K^0 \\pi^+$ decays. In the SM, the measured $\\ssb$ leads to an upper limit on $\\alpha$: $\\alpha \\leq 180^\\circ-\\beta$. Taking the weighted-average of the newest BaBar and Belle measurements of $\\spp$ and $\\app$ in $B^0 \\to \\pi^+\\pi^-$ decay as the experimental input, we find the allowed range of angle $\\alpha$, $76^\\circ \\leq \\alpha \\leq 135^\\circ$ for $r=|P/T| =0.3 \\pm 0.1 $. From the measured CP-averaged branching ratios of $B \\to \\pi^+ \\pi^-, \\pi^+ \\pi^0$ and $K^0 \\pi^+$ decays, we found an inequality, $\\cos{\\alpha} \\cos{\\delta} \\geq 0.45$. The region of $70^\\circ \\leq \\alpha \\leq 110^\\circ$ is thus excluded by applying this inequality. The combined constraints on $\\alpha$ and $\\delta$ are $117^\\circ \\leq \\alpha \\leq 135^\\circ$ and $-160^\\circ \\leq \\delta \\leq -132^\\circ$ if we take $\\spp=0.49 \\pm 0.27$ and $\\app=0.51 \\pm 0.19$ as the experimental input. The new lower limit on the angle $\\alpha$ is dominated by the measured branching ratios considered in this paper, and is much stronger than those obtained before.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2003-06-17T08:19:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "branching ratios",
      "measured cp asymmetries",
      "ckm angle",
      "experimental input",
      "experimental measurements"
    ],
    "note": {
      "typesetting": "RevTeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 614790,
      "adsabs": "2003hep.ph....3070X"
    }
  }
}