An improved light-cone harmonic oscillator model for the φ-meson longitudinal leading-twist light-cone distribution amplitude

In the present paper, we study the properties of φ-meson longitudinal leading-twist light-cone distribution amplitude φ_2;φ\|(x,μ) by starting from a light-cone harmonic oscillator model for its wavefunction. To fix the input parameters, we derive the first ten ξ-moments of φ_2;φ\|(x,μ) by using the QCD sum rules approach under the background field theory. The shape of φ_2;φ\|(x,μ=2~ GeV) tends to be a single-peak behavior, which is consistent with the latest Lattice QCD result. As an application, we derive the D⁺ₛ → φ transition form factors (TFFs) by using the light-cone sum rules approach. At the large recoil point, we obtain A₁(0) = 0.512-0.020+0.030, A₂(0) = 0.402-0.067+0.078, A₀(0) = 0.596-0.020+0.025 and V(0) = 0.882-0.036+0.040. As for the two typical ratios γV and γ₂, we obtain γV = 1.723-0.021+0.023 and γ₂ = 0.785-0.104+0.100. After extrapolating those TFFs to the physically allowable region, we then obtain the transverse, longitudinal and total decay widths for semi-leptonic decay D⁺ₛ→φ⁺ν_. Then the branching fractions are B(D⁺ₛ→ φ e⁺νₑ) = (2.367-0.132+0.256)× 10⁻³ and B(D⁺ₛ→ φ μ⁺νμ) = (2.349-0.132+0.255)× 10⁻³, which show good agreement with the data issued by the BESIII, the CLEO, and the BABAR Collaborations. We finally calculate D⁺ₛ→φ⁺ ν_ polarization and asymmetry parameters.