Probing |V₂ₒ| and lepton flavor universality through D K₀^ (1430) _ decay

In this paper, we calculate the semileptonic decay D K₀^ (1430) _ with = (e, ) induced by c s_ 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 10th-order -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) ^-_ and D^+ K₀^ 0 (1430) ^+_ which at 10^-4-order level for the S1 and S2 cases. Meanwhile, we predict the CKM matrix |V₂ₒ|^ (S1) =0. 997^+0. 258-₀. ₁₇₂, |V₂ₒ|^ (S2) =0. 903^+0. 233-₀. ₁₅₅, and leptonic flavour universality R^ (S1) ₊䃐^*=0. 768^+0. 560-₀. ₃₆₈, R₊䃐^*^ (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.