{
  "id": "2302.07048",
  "version": "v1",
  "published": "2023-02-14T14:03:16.000Z",
  "updated": "2023-02-14T14:03:16.000Z",
  "title": "Study of $^{113}$Cd $β$-decay spectrum and $g_{\\rm A}$ quenching using spectral moments",
  "authors": [
    "Joel Kostensalo",
    "Eligio Lisi",
    "Antonio Marrone",
    "Jouni Suhonen"
  ],
  "comment": "13 pages, including 5 figures and 2 tables",
  "categories": [
    "nucl-th",
    "hep-ex",
    "hep-ph",
    "nucl-ex"
  ],
  "abstract": "We present an alternative analysis of the $^{113}$Cd $\\beta$-decay electron energy spectrum in terms of spectral moments $\\mu_n$, corresponding to the averaged values of $n^{\\rm th}$ powers of the $\\beta$ particle energy. The zeroth moment $\\mu_0$ is related to the decay rate, while higher moments $\\mu_n$ are related to the spectrum shape. The here advocated spectral-moment method (SMM) allows for a complementary understanding of previous results, obtained using the so-called spectrum-shape method (SSM) and its revised version, in terms of two free parameters: $r=g_{\\rm A}/g_{\\rm V}$ (the ratio of axial-vector to vector couplings) and $s$ (the small vector-like relativistic nuclear matrix element, $s$-NME). We present numerical results for three different nuclear models with the conserved vector current hypothesis (CVC) assumption of $g_{\\rm V}=1$. We show that most of the spectral information can be captured by the first few moments which are simple quadratic forms (conic sections) in the $(r,\\,s)$ plane: an ellipse for $n=0$ and hyperbolae for $n\\geq 1$, all being nearly degenerate as a result of cancellations among nuclear matrix elements. The intersections of these curves, as obtained by equating theoretical and experimental values of $\\mu_n$, identify the favored values of $(r,\\,s)$ at a glance, without performing detailed fits. In particular, we find that values around $r\\sim 1$ and $s\\sim 1.6$ are consistently favored in each nuclear model, confirming the evidence for $g_{\\rm A}$ quenching in $^{113}$Cd, and shedding light on the role of the $s$-NME. We briefly discuss future applications of the SMM to other forbidden $\\beta$-decay spectra sensitive to $g_{\\rm A}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-02-14T14:03:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "decay spectrum",
      "spectral moments",
      "vector-like relativistic nuclear matrix element",
      "decay electron energy spectrum",
      "nuclear model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}