First Measurement of the Decay Dynamics in the Semileptonic Transition of the D⁺⁽⁰⁾ into the Axial-vector Meson K₁(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⁺→ K₁(1270)⁰ e⁺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⁺→ K₁(1400)⁰ e⁺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.