Probing |Vcs| and lepton flavor universality through $D→ K_0^(1430)ν_{}$ decay

In this paper, we calculate the semileptonic decay D→ K₀⁽1430)ν_ with =(e,μ) induced by c→ sν_ transition. For the key component, D→ K₀⁽1430) transition form factors (TFFs) f±(q²) are calculated within the framework of QCD light-cone sum rule. Then, we consider two scenarios for K₀⁽1430)-meson twist-2 distribution amplitude. For the scenario 1 (S1), we take the truncated form based on Gegenbauer polynomial series. Meanwhile, we also consider the scenario 2 (S2) constructed by light-cone harmonic oscillator model, where the model parameters are fixed by the K₀⁽1430)-meson twist-2 distribution amplitude $10$th-order ξ-moments calculated by using the background field theory. For the TFFs at large recoil point, we have f₊(S1)(0)=0.597+0.122-0.121 and f₋(S1)(0)=-0.136+0.023-0.035, f₊(S2)(0)= 0.663+0.135-0.134 and f₋(S2)(0)=-0.202+0.026-0.046. After extrapolating TFFs to the whole physical q²-region, we calculate the branching fractions of D⁰→ K₀⁺(1430)⁻ν_ and D⁺→ K₀⁰(1430)⁺ν_ which at 10⁻⁴-order level for the S1 and S2 cases. Meanwhile, we predict the CKM matrix |Vcs|(S1)=0.997+0.258-0.172, |Vcs|(S2)=0.903+0.233-0.155, and leptonic flavour universality R(S1)K₀^*=0.768+0.560-0.368, RK₀^*(S2)=0.764+0.555-0.365. Finally, we discuss the angular observables of forward-backward asymmetries, lepton polarization asymmetries and q²-differential flat terms for this decay.