Scrutinizing lepton flavor universality and transition form factor correlation from charmed meson semileptonic decay into light strange vector $K^*$ meson

In this paper, we calculate the transition form factors (TFFs) $A_{1,2}(q^2)$ and $V(q^2)$ of $D_s^+ \to K^{*0}$ decays by using the QCD light-cone sum rule (QCD LCSR) and constructing a correlation function containing the usual current, in which the twist-2 transverse and longitudinal light-cone distribution amplitudes (LCDAs) $\phi^\lambda_{2;K^{*0}}(x,\mu_0)$ with $\lambda=(\bot,\|)$ of the $K^{*0}$ meson constitute the main source of theoretical uncertainty. Based on this, we construct these LCDAs using the light-cone harmonic oscillator model. Subsequently, the TFFs obtained in the large recoil region are $A_{1}(0)=0.579_{-0.028}^{+0.024}$, $A_{2}(0)=0.414_{-0.023}^{+0.021}$, and $V(0)=0.830_{-0.020}^{+0.020}$, and the corresponding ratios are obtained to be $r_V=1.433_{-0.090}^{+0.110}$ and $r_2=0.715_{-0.067}^{+0.075}$. Furthermore, we predict the correlation of TFFs and their corresponding ratios. Then, we extrapolate the TFFs over the whole physical $q^2$-region and calculate the decay widths and branching fractions for the semileptonic decays $D_s^+\to K^{*0}\ell^+\nu_{\ell}$. The results are $\mathcal{B}(D_s^+\to K^{*0}e^+\nu_{e})=(2.05_{-0.16}^{+0.13})\times 10^{-3}$ and $\mathcal{B}(D_s^+\to K^{*0}\mu^+\nu_{\mu})=(1.95_{-0.15}^{+0.13})\times 10^{-3}$. Meanwhile, we calculated the branching fraction ratio $\mathcal{R}_{\mu/e}^{K^{*0}}$ to be $0.950_{-0.002}^{+0.004}$. In addition, we extract values of the CKM matrix element, obtaining $|V_{cd}|_{(e\text{-Channel})} = 0.225_{-0.005}^{+0.005}$ and $|V_{cd}|_{(\mu\text{-Channel})} = 0.227_{-0.004}^{+0.011}$. Finally, we calculated the forward-backward asymmetry parameters for the $D_s^+\to K^{*0} \ell^+\nu_{\ell}$ decay.