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In this paper, we carry out an investigation into the semileptonic decays Dₛ^+ K⁰^+_ with = (e, ) by employing the QCD light-cone sum rules approach. The vector transition form factor (TFF) f_+^Dₛ^+ K⁰ (q²) for Dₛ^+ K⁰ decay is calculated while considering its next-to-leading order contribution. Subsequently, we briefly introduce the twist-2, 3 kaon distribution amplitudes, which are calculated by using QCD sum rules within the framework of the background field theory. At the large recoil point, the TFF has f_+^Dₛ^+ K⁰ (0) =0. 692-₀. ₀₂₆^+0. 027. Then, we extrapolate f_+^Dₛ^+ K⁰ (q²) to the whole physical q²-region via the simplified z (q², t) -series expansion, and the behavior of TFF f_+^Dₛ^+ K⁰ (q²) is exhibited in the numerical results part, including the theoretical and experimental predictions for comparison. In addition, we compute the differential branching fraction B (Dₛ^+ K⁰^+_) with the electron and muon channels, which are expected to be B (Dₛ^+ K⁰e^+ₑ) =3. 379-₀. ₂₇₅^+0. 301 10^-3 and B (Dₛ^+ K⁰^+_) =3. 351-₀. ₂₇₃^+0. 299 10^-3 as well as contained other results for comparison. Our results show good agreement with the BESIII measurements and theoretical predictions. Furthermore, we present our prediction with respect to the CKM matrix element |V₂₃| by using the B (Dₛ^+ K⁰e^+ₑ) result from BESIII Collaboration, yielding |V₂₃|=0. 221-₀. ₀₁₀^+0. 008. Finally, we provide the ratio between Dₛ^+ K⁰e^+ₑ and Dₛ^+ e^+ₑ channels, i. e. R₊䃀/ᵉ=0. 144-₀. ₀₂₀^+0. 028.
Tian et al. (Sun,) studied this question.