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Light-cone sum rules analysis of the semileptonic $D_{s}^{+} \to f_{0} (980) (\to π^{+} π^{-}) e^{+} ν_{e}$ decay incorporating the $f_{0} (980)$ mixing state twist-2 distribution amplitudes

Dan-Dan Hu and Xing-Gang Wu

Hai-Jiang Tian

Tao Zhong ^* and Hai-Bing Fu

Department of Physics, Chongqing Key Laboratory for Strongly Coupled Physics, Chongqing University, Chongqing 401331, People’s Republic of China

Department of Physics, Guizhou Minzu University, Guiyang 550025, People’s Republic of China

Department of Physics, Guizhou Minzu University, Guiyang 550025, People’s Republic of China and Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, People’s Republic of China

^*Contact author: zhongtao@gzmu.edu.cn

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Phys. Rev. D 112, 056023 – Published 19 September, 2025

DOI: https://doi.org/10.1103/49qx-p3pl

Abstract

The isospin-singlet scalar meson $f_{0} (980)$ is hypothesized to consist of two energy eigenstates, forming a mixture of $\frac{1}{\sqrt{2}} (\bar{u} u + \bar{d} d)$ and $\bar{s} s$ . Building on this framework, we apply the quantum chromodynamics (QCD) sum rules approach in the background field theory to compute the $f_{0} (980)$ decay constant, yielding $f_{f_{0}} (μ_{0} = 1 GeV) = 0.386 \pm 0.009 GeV$ . Subsequently, we derive the first two $ξ$ -moments of the leading-twist light-cone distribution amplitude $ϕ_{2; f_{0}}$ . Using QCD light-cone sum rules, we then calculate the $D_{s}^{+} \to f_{0} (980)$ transition form factor (TFF) $f_{+} (q^{2})$ , obtaining $f_{+} (0) = 0.51 6_{- 0.024}^{+ 0.027}$ at the large-recoil region. We extend $f_{+} (q^{2})$ to the full physical region via a simplified series expansion parametrization, enabling calculations of the differential decay widths and the branching fraction $B (D_{s}^{+} \to f_{0} (980) (\to π^{+} π^{-}) e^{+} ν_{e}) = (1.78 3_{- 0.189}^{+ 0.227}) \times 10^{- 3}$ . Our theoretical predictions align well with the latest BESIII Collaboration measurements within reasonable errors.

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Phys. Rev. D 112, 056023– Published 19 September, 2025

Vol. 112, Iss. 5 — 1 September 2025

Received 23 June 2025
Accepted 2 September 2025

DOI: https://doi.org/10.1103/49qx-p3pl

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

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Light-cone sum rules analysis of the semileptonic $D_{s}^{+} \to f_{0} (980) (\to π^{+} π^{-}) e^{+} ν_{e}$ decay incorporating the $f_{0} (980)$ mixing state twist-2 distribution amplitudes

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Light-cone sum rules analysis of the semileptonic Ds+→f0(980)(→π+π−)e+νe decay incorporating the f0(980) mixing state twist-2 distribution amplitudes

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References (82)

Light-cone sum rules analysis of the semileptonic $D_{s}^{+} \to f_{0} (980) (\to π^{+} π^{-}) e^{+} ν_{e}$ decay incorporating the $f_{0} (980)$ mixing state twist-2 distribution amplitudes