First Measurement of the Decay Dynamics in the Semileptonic Transition of D+ (0) into the Axial-Vector Meson K ¯ 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+π0(-)e+νe. The amplitude analysis gives the hadronic form factors of the semileptonic D transitions into the axial-vector meson K̄1(1270) to be rA=(-11.2±1.0stat±0.9syst)×10-2 and rV=(-4.3±1.0stat±2.5syst)×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 Aud′=0.01±0.11, which is consistent with the standard model prediction. In addition, the branching fractions of D+→K̄1(1270)0e+νe and D0→K1(1270)-e+νe are determined with improved precision to be (2.27±0.11stat±0.07syst±0.07input)×10-3 and (1.02±0.06stat±0.06syst±0.03input)×10-3, respectively. No significant signals of D+→K̄1(1400)0e+νe and D0→K1(1400)-e+νe 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.