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Study of the ${f}_{0}\left(980\right)$ and ${f}_{0}\left(500\right)$ Scalar Mesons through the Decay ${D}_{s}^{+}\to {\pi }^{+}{\pi }^{-}{e}^{+}{\nu }_{e}$

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{
  "DOI": "10.1103/PhysRevLett.132.141901", 
  "abstract": "<p>Using ${e}^{+}{e}^{-}$ collision data corresponding to an integrated luminosity of $7.33\\text{}\\text{}{\\mathrm{fb}}^{-1}$ recorded by the BESIII detector at center-of-mass energies between 4.128 and 4.226 GeV, we present an analysis of the decay ${D}_{s}^{+}\\to {\\pi }^{+}{\\pi }^{-}{e}^{+}{\\nu }_{e}$, where the ${D}_{s}^{+}$ is produced via the process ${e}^{+}{e}^{-}\\to {D}_{s}^{*\u00b1}{D}_{s}^{\\mp }$. We observe the ${f}_{0}\\left(980\\right)$ in the ${\\pi }^{+}{\\pi }^{-}$ system and the branching fraction of the decay ${D}_{s}^{+}\\to {f}_{0}\\left(980\\right){e}^{+}{\\nu }_{e}$ with ${f}_{0}\\left(980\\right)\\to {\\pi }^{+}{\\pi }^{-}$ measured to be $\\left(1.72\u00b10.1{3}_{\\mathrm{stat}}\u00b10.1{0}_{\\mathrm{syst}}\\right)\u00d7{10}^{-3}$, where the uncertainties are statistical and systematic, respectively. The dynamics of the ${D}_{s}^{+}\\to {f}_{0}\\left(980\\right){e}^{+}{\\nu }_{e}$ decay are studied with the simple pole parametrization of the hadronic form factor and the Flatt\u00e9 formula describing the ${f}_{0}\\left(980\\right)$ in the differential decay rate, and the product of the form factor ${f}_{+}^{{f}_{0}}\\left(0\\right)$ and the $c\\to s$ Cabibbo-Kobayashi-Maskawa matrix element $|{V}_{cs}|$ is determined for the first time to be ${f}_{+}^{{f}_{0}}\\left(0\\right)|{V}_{cs}|=0.504\u00b10.01{7}_{\\mathrm{stat}}\u00b10.03{5}_{\\mathrm{syst}}$. Furthermore, the decay ${D}_{s}^{+}\\to {f}_{0}\\left(500\\right){e}^{+}{\\nu }_{e}$ is searched for the first time but no signal is found. The upper limit on the branching fraction of ${D}_{s}^{+}\\to {f}_{0}\\left(500\\right){e}^{+}{\\nu }_{e}$, ${f}_{0}\\left(500\\right)\\to {\\pi }^{+}{\\pi }^{-}$ decay is set to be $3.3\u00d7{10}^{-4}$ at 90% confidence level.</p>", 
  "author": [
    {
      "family": "CERN \u0130\u015fbirli\u011fi"
    }
  ], 
  "container_title": "Physical Review Letters", 
  "id": "275157", 
  "issue": "14", 
  "issued": {
    "date-parts": [
      [
        2024, 
        4, 
        5
      ]
    ]
  }, 
  "title": "Study of the ${f}_{0}\\left(980\\right)$ and ${f}_{0}\\left(500\\right)$ Scalar Mesons through the Decay ${D}_{s}^{+}\\to {\\pi }^{+}{\\pi }^{-}{e}^{+}{\\nu }_{e}$", 
  "type": "article-journal", 
  "volume": "132"
}
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