First Measurement of the Decay Dynamics in the Semileptonic Transition of D^{+(0)} into the Axial-Vector Meson K[over ¯]_{1}(1270)

Using e^{+}e^{-} data taken at the center-of-mass energy of 3.773 GeV with the BESIII detector, corresponding to an integrated luminosity of 20.3  fb^{-1}, we report the first measurement of the decay dynamics of the semileptonic decays D^{+(0)}→K^{-}π^{+}π^{0(-)}e^{+}ν_{e}. The amplitude analysis gives the hadronic form factors of the semileptonic D transitions into the axial-vector meson K[over ¯]_{1}(1270) to be r_{A}=(-11.2±1.0_{stat}±0.9_{syst})×10^{-2} and r_{V}=(-4.3±1.0_{stat}±2.5_{syst})×10^{-2}. This is the first in the semileptonic decays of heavy mesons into axial-vector mesons. The angular analysis yields an up-down asymmetry A_{ud}^{'}=0.01±0.11, which is consistent with the standard model prediction. In addition, the branching fractions of D^{+}→K[over ¯]_{1}(1270)^{0}e^{+}ν_{e} and D^{0}→K_{1}(1270)^{-}e^{+}ν_{e} are determined with improved precision to be (2.27±0.11_{stat}±0.07_{syst}±0.07_{input})×10^{-3} and (1.02±0.06_{stat}±0.06_{syst}±0.03_{input})×10^{-3}, respectively. No significant signals of D^{+}→K[over ¯]_{1}(1400)^{0}e^{+}ν_{e} and D^{0}→K_{1}(1400)^{-}e^{+}ν_{e} are observed and their branching fraction upper limits are set as 1.4×10^{-4} and 0.7×10^{-4} at 90% confidence level, respectively.