{
  "id": "2305.03885",
  "version": "v1",
  "published": "2023-05-06T00:48:39.000Z",
  "updated": "2023-05-06T00:48:39.000Z",
  "title": "$φ(2170)$ decaying to $φη$ and $φη^\\prime$",
  "authors": [
    "Brenda B. Malabarba",
    "K. P. Khemchandani",
    "A. Martinez Torres"
  ],
  "categories": [
    "hep-ph",
    "nucl-th"
  ],
  "abstract": "In this work we calculate the decay widths of $\\phi(2170)$ to $\\phi\\eta$ and $\\phi\\eta^\\prime$ by considering $\\phi(2170)$ as a $\\phi K\\bar K$ state, with $K\\bar K$ clustering as $f_0(980)$. These decay widths have been recently determined by the BESIII, BaBar and Belle collaborations with the aim of unraveling the nature of $\\phi(2170)$. By analyzing the data on the cross sections of the process $e^+e^-\\to\\phi\\eta$, two solutions were found by the BESIII collaboration with the same $\\chi^2/n.d.f$, mass and width for $\\phi(2170)$. However, different values for $\\mathcal{B}^{\\phi(2170)}_{\\phi\\eta}\\Gamma^{\\phi(2170)}_{e^+e^-}$ were obtained: $0.24^{+0.12}_{-0.07}$ eV (solution I) and $10.11^{+3.87}_{-3.13}$ eV (solution II). In case of $\\mathcal{B}^{\\phi(2170)}_{\\phi\\eta^\\prime}\\Gamma^{\\phi(2170)}_{e^+e^-}$, a value of $7.1\\pm 0.7\\pm 0.7$ was determined by the BESIII collaboration from fits to the data on the cross section of $e^+e^-\\to\\phi\\eta^\\prime$. The Belle collaboration has also determined $\\mathcal{B}^{\\phi(2170)}_{\\phi\\eta}\\Gamma^{\\phi(2170)}_{e^+e^-}$ more recently, although the statistical significance related to the signal of $\\phi(2170)$ in the data is low. We calculate the decay widths of $\\phi(2170)$ to $\\phi\\eta$ and $\\phi\\eta^\\prime$, and compare their ratio $\\Gamma^{\\phi(2170)}_{\\phi \\eta}/\\Gamma^{\\phi(2170)}_{\\phi \\eta^\\prime}$ with the one determined by using the above mentioned experimental data. Considering the theoretical and experimental uncertainties, the lower limit of our theoretical result ($\\simeq 2.6$) is close to the upper value obtained ($\\simeq 2$) by using the solution II of BESIII for $\\mathcal{B}^{\\phi(2170)}_{\\phi\\eta}\\Gamma^{\\phi(2170)}_{e^+e^-}$, as well as to the upper limit found ($\\simeq 2.8$) when considering the solutions III and IV of the Belle collaboration for $\\mathcal{B}^{\\phi(2170)}_{\\phi\\eta}\\Gamma^{\\phi(2170)}_{e^+e^-}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-06T00:48:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "belle collaboration",
      "decay widths",
      "besiii collaboration",
      "cross section",
      "upper limit"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}