{
  "id": "hep-ph/0412144",
  "version": "v1",
  "published": "2004-12-10T16:03:32.000Z",
  "updated": "2004-12-10T16:03:32.000Z",
  "title": "Sum rules in the heavy quark limit of QCD and Isgur-Wise functions",
  "authors": [
    "F. Jugeau",
    "A. Le Yaouanc",
    "L. Oliver",
    "J. -C. Raynal"
  ],
  "comment": "Talk given at the ICHEP04 Conference (Beijing, August 2004)",
  "categories": [
    "hep-ph"
  ],
  "abstract": "Using the OPE, we formulate new sum rules in the heavy quark limit of QCD. These sum rules imply that the elastic Isgur-Wise function $\\xi (w)$ is an alternate series in powers of $(w-1)$. Moreover, one gets that the $n$-th derivative of $\\xi (w)$ at $ w=1$ can be bounded by the $(n-1)$-th one, and an absolute lower bound for the $n$-th derivative $(-1)^n \\xi^{(n)}(1) \\geq {(2n+1)!! \\over 2^{2n}}$. Moreover, for the curvature we find $\\xi ''(1) \\geq {1 \\over 5} [4 \\rho^2 + 3(\\rho^2)^2]$ where $\\rho^2 = - \\xi '(1)$. We show that the quadratic term ${3 \\over 5} (\\rho^2)^2$ has a transparent physical interpretation, as it is leading in a non-relativistic expansion in the mass of the light quark. These bounds should be taken into account in the parametrizations of $\\xi (w)$ used to extract $|V_{cb}|$. These results are consistent with the dispersive bounds, and they strongly reduce the allowed region of the latter for $\\xi (w)$. The method is extended to the subleading quantities in $1/m_Q$, namely $\\xi_3(w)$ and $\\bar{\\Lambda}\\xi (w)$.}]",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-12-10T16:03:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "heavy quark limit",
      "sum rules",
      "absolute lower bound",
      "light quark",
      "non-relativistic expansion"
    ],
    "tags": [
      "conference paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 666739
    }
  }
}