Searching for $|V_{cd}|$ through the exclusive decay $D_s^+ \to K^0e^+ν_e$ within QCD Sum Rules

Abstract

In this paper, we carry out an investigation into the semileptonic decays $D_s^+ \to K^0\ell^+ν_\ell$ with $\ell=(e,μ)$ by employing the QCD light-cone sum rules approach. The vector transition form factor (TFF) $f_+^{D_s^+ K^0}(q^2)$ for $D_s^+\to K^0$ 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 $\mathcal{B}(D_s^+ \to K^0\ell^+ν_\ell)$ with the electron and muon channels, which are expected to be $\mathcal{B}(D_s^+ \to K^0e^+ν_e)=3.379_{-0.275}^{+0.301}\times 10^{-3}$ and $\mathcal{B}(D_s^+ \to K^0μ^+ν_μ)=3.351_{-0.273}^{+0.299}\times 10^{-3}$ 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 $\mathcal{B}(D_s^+ \to K^0e^+ν_e)$ result from BESIII Collaboration, yielding $|V_{cd}|=0.221_{-0.010}^{+0.008}$. Finally, we provide the ratio between $D_s^+ \to K^0e^+ν_e$ and $D_s^+ \to ηe^+ν_e$ channels, i.e. $\mathcal{R}_{K^0/η}^e=0.144_{-0.020}^{+0.028}$.