{
  "id": "hep-ph/9703268",
  "version": "v2",
  "published": "1997-03-07T17:44:25.000Z",
  "updated": "1997-07-08T08:12:20.000Z",
  "title": "Resummation analysis of the $τ$ decay width using the four-loop $β$-function",
  "authors": [
    "S. Groote",
    "J. G. Körner",
    "A. A. Pivovarov"
  ],
  "comment": "12 pages, LaTeX, more detailed explanation of the analysis done for the determination of the convergence radius, one PostScript figure added",
  "journal": "Mod.Phys.Lett. A13 (1998) 637-650",
  "doi": "10.1142/S0217732398000693",
  "categories": [
    "hep-ph"
  ],
  "abstract": "We extract the strong coupling constant $\\alpha_s(m_\\tau^2)$ from the semileptonic $\\tau$ decay width taking into account resummation effects from the running of the strong coupling constant. In the $\\overline{\\rm MS}$ scheme the result reads $\\alpha_s=0.375\\pm 0.007$ to third order and $\\alpha_s=0.378\\pm 0.007$ to fourth order in the $\\beta$-function, respectively, where we use the recently computed four-loop coefficient $\\beta_3$. These values for the coupling constant have to be compared with the value $\\alpha_s=0.354\\pm 0.005$ derived from a third order analysis of $\\tau$ decays. We determine the exact value of the convergence radius of the perturbation series by analyzing the singularity structure of the complex coupling constant plane.",
  "revisions": [
    {
      "version": "v2",
      "updated": "1997-07-08T08:12:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "decay width",
      "resummation analysis",
      "strong coupling constant",
      "account resummation effects",
      "complex coupling constant plane"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 441015
    }
  }
}