Observation of D^{+}→η^{'}μ^{+}ν_{μ} and First Experimental Study of D^{+}→η^{'}ℓ^{+}ν_{ℓ} Decay Dynamics.

Using 20.3  fb^{-1} of e^{+}e^{-} collision data collected at the center-of-mass energy 3.773 GeV with the BESIII detector, we report the first observation of the semileptonic decay D^{+}→η^{'}μ^{+}ν_{μ} with significance of 8.6σ including systematic uncertainties, and an improved measurement of D^{+}→η^{'}e^{+}ν_{e}. The branching fractions of D^{+}→η^{'}μ^{+}ν_{μ} and D^{+}→η^{'}e^{+}ν_{e} are determined to be (1.92±0.28_{stat}±0.08_{syst})×10^{-4} and (1.79±0.19_{stat}±0.07_{syst})×10^{-4}, respectively. The ratio of the two branching fractions is determined to be R_{μ/e}=1.07±0.19_{stat}±0.03_{syst}, which agrees with the theoretical expectation of lepton flavor universality within the standard model. From an analysis of the D^{+}→η^{'}ℓ^{+}ν_{ℓ} decay dynamics, the product of the hadronic form factor f_{+}^{η^{'}}(0) and the Cabibbo-Kobayashi-Maskawa matrix element |V_{cd}| is measured for the first time, giving f_{+}^{η^{'}}(0)|V_{cd}|=(5.92±0.56_{stat}±0.13_{syst})×10^{-2}. The η-η^{'} mixing angle in the quark flavor basis is determined to be ϕ_{P}=(39.8±0.8_{stat}±0.3_{syst})°.