# Study of dynamics of D^{0}→K−e+νe and D^{0}→π−e+νe decays

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 B(D0→K−e+νe)=(3.505±0.014±0.033)% and B(D0→π−e+νe)=(0.295±0.004±0.003)%. From a study of the differential decay rates we obtain the products of hadronic form factor and the magnitude of the Cabibbo-Kobayashi- Maskawa (CKM) matrix element fK+(0)|Vcs|=0.7172±0.0025±0.0035 and fπ+(0)|Vcd|=0.1435±0.0018±0.0009. Combining these products with the values of |Vcs(d)| from the SM constraint fit, we extract the hadronic form factors fK+(0)=0.7368±0.0026±0.0036 and fπ+(0)=0.6372±0.0080±0.0044, and their ratio fπ+(0)/fK+(0)=0.8649±0.0112±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 fK(π)+(0)|Vcs(d)| and the lattice QCD value for fK(π)+(0) are used to extract values of the CKM matrix elements of |Vcs|=0.9601±0.0033±0.0047±0.0239 and |Vcd|=0.2155±0.0027±0.0014±0.0094, where the third errors are due to the uncertainties in lattice QCD calculations of the form factors. Using the LCSR value for fπ+(0)/fK+(0), we determine the ratio |Vcd|/|Vcs|=0.238±0.004±0.002±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.