In an analysis of a 2.92~fb$^{-1}$ data sample taken at 3.773~GeV with the BESIII detector operated at the BEPCII collider, we measure the absolute decay branching fractions to be $mathcal B(D^0 to K^-e^+ u_e)=(3.505pm 0.014 pm 0.033)%$ and $mathcal B(D^0 to pi^-e^+ u_e)=(0.295pm 0.004pm 0.003)%$. From a study of the differential decay rates we obtain the products of hadronic form factor and the magnitude of the CKM matrix element $f_{+}^K(0)|V_{cs}|=0.7172pm0.0025pm 0.0035$ and $f_{+}^{pi}(0)|V_{cd}|=0.1435pm0.0018pm 0.0009$. Combining these products with the values of $|V_{cs(d)}|$ from the SM constraint fit, we extract the hadronic form factors $f^K_+(0) = 0.7368pm0.0026pm 0.0036$ and $f^pi_+(0) = 0.6372pm0.0080pm 0.0044$, and their ratio $f_+^{pi}(0)/f_+^{K}(0)=0.8649pm 0.0112pm 0.0073$. These form factors and their ratio are used to test unquenched Lattice QCD calculations of the form factors and a light cone sum rule (LCSR) calculation of their ratio. The measured value of $f_+^{K(pi)}(0) |V_{cs(d)}|$ and the lattice QCD value for $f^{K(pi)}_+(0)$ are used to extract values of the CKM matrix elements of $|V_{cs}|=0.9601 pm 0.0033 pm 0.0047 pm 0.0239$ and $|V_{cd}|=0.2155 pm 0.0027 pm 0.0014 pm 0.0094$, where the third errors are due to the uncertainties in lattice QCD calculations of the form factors. Using the LCSR value for $f_+^pi(0)/f_+^K(0)$, we determine the ratio $|V_{cd}|/|V_{cs}|=0.238pm 0.004pm 0.002pm 0.011$, where the third error is from the uncertainty in the LCSR normalization. In addition, we measure form factor parameters for three different theoretical models that describe the weak hadronic charged currents for these two semileptonic decays. All of these measurements are the most precise to date.
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