Searching for |V_cd| through the exclusive decay D_s^+ → K^0e^+ν_e within QCD Sum Rules

In this paper, we carry out an investigation into the semileptonic decays D_s^+ → K^0ℓ^+ν_ℓ with ℓ=(e,μ) by employing the QCD light-cone sum rules approach. The vector transition form factor (TFF) f_+^D_s^+ K^0(q^2) for D_s^+→ K^0 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_+^D_s^+ K^0(0)=0.692_-0.026^+0.027. Then, we extrapolate f_+^D_s^+ K^0(q^2) to the whole physical q^2-region via the simplified z(q^2,t)-series expansion, and the behavior of TFF f_+^D_s^+ K^0(q^2) is exhibited in the numerical results part, including the theoretical and experimental predictions for comparison. In addition, we compute the differential branching fraction ℬ(D_s^+ → K^0ℓ^+ν_ℓ) with the electron and muon channels, which are expected to be ℬ(D_s^+ → K^0e^+ν_e)=3.379_-0.275^+0.301× 10^-3 and ℬ(D_s^+ → K^0μ^+ν_μ)=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 |V_cd| by using the ℬ(D_s^+ → K^0e^+ν_e) result from BESIII Collaboration, yielding |V_cd|=0.221_-0.010^+0.008. Finally, we provide the ratio between D_s^+ → K^0e^+ν_e and D_s^+ →η e^+ν_e channels, i.e. ℛ_K^0/η^e=0.144_-0.020^+0.028.