Light-cone sum rules analysis of the semileptonic D⁺_s → f₀(980) (→ π⁺ π⁻)e⁺ ν_e decay incorporating the f ₀(980) mixing state twist-2 distribution amplitudes

The isospin-singlet scalar meson (Formula presented) is hypothesized to consist of two energy eigenstates, forming a mixture of (Formula presented). Building on this framework, we apply the quantumchromodynamics (QCD) sum rules approach in the background field theory to compute the (Formula presented) decay constant, yielding ff0 (Formula presented). Subsequently, we derive the first two ξ-moments of the leadingtwist light-cone distribution amplitude (Formula presented). Using QCD light-cone sum rules, we then calculate the (Formula presented) transition form factor (TFF) (Formula presented), obtaining (Formula presented) at the large-recoil region. We extend f (Formula presented) to the full physical region via a simplified series expansion parametrization, enabling calculations of the differential decay widths and the branching fraction(Formula presented). Our theoretical predictions align well with the latest BESIII Collaboration measurements within reasonable errors.