{
  "id": "hep-ph/0210231",
  "version": "v2",
  "published": "2002-10-16T14:29:45.000Z",
  "updated": "2002-11-06T16:42:56.000Z",
  "title": "Bounds on the derivatives of the Isgur-Wise function from sum rules in the heavy quark limit of QCD",
  "authors": [
    "A. Le Yaouanc",
    "L. Oliver",
    "J. -C. Raynal"
  ],
  "comment": "9 pages, Latex",
  "journal": "Phys.Lett. B557 (2003) 207-212",
  "doi": "10.1016/S0370-2693(03)00180-1",
  "categories": [
    "hep-ph"
  ],
  "abstract": "Using the OPE and the trace formalism, we have obtained a number of sum rules in the heavy quark limit of QCD that include the sum over all excited states for any value $j^P$ of the light cloud. We show that these sum rules imply that the elastic Isgur-Wise function $\\xi (w)$ is an alternate series in powers of $(w-1)$. Moreover, we obtain sum rules involving the derivatives of the elastic Isgur-Wise function $\\xi (w)$ at zero recoil, that imply that the $n$-th derivative can be bounded by the $(n-1)$-th one. For the curvature $\\sigma^2 = \\xi''(1)$, this proves the already proposed bound $\\sigma^2 \\geq {5 \\over 4} \\rho^2$. Moreover, we obtain the absolute bound for the $n$-th derivative $(-1)^n \\xi^{(n)}(1) \\geq {(2n+1)!! \\over 2^{2n}}$, that generalizes the results $\\rho^2 \\geq {3 \\over 4}$ and $\\sigma^2 \\geq {15 \\over 16}$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2002-11-06T16:42:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "heavy quark limit",
      "sum rules",
      "elastic isgur-wise function",
      "th derivative",
      "light cloud"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 599935
    }
  }
}