{
  "id": "hep-ph/9804201",
  "version": "v1",
  "published": "1998-04-01T03:48:41.000Z",
  "updated": "1998-04-01T03:48:41.000Z",
  "title": "A new order $α$ correction to the decay rate of pionium",
  "authors": [
    "P. Labelle",
    "K. Buckley"
  ],
  "comment": "7 pages, 5 Postscript figures, uses Revtex V3.0 and epsf.tex",
  "categories": [
    "hep-ph"
  ],
  "abstract": "Recently, much work has been devoted to the calculation of order $\\alpha$ corrections to the decay rate of pionium, the $\\pi^+ \\pi^-$ bound state. In previous calculations, nonrelativistic QED corrections were neglected since they start at order $\\alpha^2$ in hydrogen and positronium. In this note, we point out that there is one correction which is actually of order $\\alpha$ times a function of the ratio $\\mu_r \\alpha / m_e$, where $\\mu_r$ is the reduced mass of the system. When $\\mu_r \\alpha \\ll m_e$, this function can be Taylor expanded and leads to higher order corrections. When $\\mu_r \\alpha \\approx m_e$, as is the case in pionium, the function is of order one and the correction is of order $\\alpha$. We use an effective field theory approach to calculate this correction and find it equal to $0.4298 \\alpha \\Gamma_0$. We also calculate the corresponding correction to the dimuonium ($\\mu^+ \\mu^-$ bound state) decay rate and obtained a result in agreement with Jentschura et al.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1998-04-01T03:48:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "decay rate",
      "bound state",
      "higher order corrections",
      "effective field theory approach",
      "nonrelativistic qed corrections"
    ],
    "note": {
      "typesetting": "RevTeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 468805,
      "adsabs": "1998hep.ph....4201L"
    }
  }
}