Observation of $D^+\toη^\primeμ^+ν_μ$ and First Study of $D^+\to η^\prime \ell^+ν_\ell$ Decay Dynamics
Using $20.3\,\rm fb^{-1}$ 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 $D^+\to η^\prime μ^+ν_μ$ with significance of $8.6σ$ including systematic uncertainties, and an improved measurement of $D^+\to η^\prime e^+ν_e$. The branching fractions of $D^+\to η^\prime μ^+ν_μ$ and $D^+\to η^\prime e^+ν_e$ are determined to be $(1.92\pm0.28_{\rm stat}\pm 0.08_{\rm syst})\times 10^{-4}$ and $(1.79\pm0.19_{\rm stat}\pm 0.07_{\rm syst})\times 10^{-4}$, respectively. The ratio of the two branching fractions is determined to be ${\mathcal R}_{μ/e}=1.07\pm0.19_{\rm stat}\pm 0.03_{\rm syst}$, which agrees with the theoretical expectation of lepton flavor universality within the Standard Model.From an analysis of the $D^+\to η^\prime \ell^+ν_\ell$ decay dynamics, the product of the hadronic form factor $f_+^{η^{\prime}}(0)$ and the CKM matrix element $|V_{cd}|$ is measured for the first time, giving $f^{η^\prime}_+(0)|V_{cd}| = (5.92\pm0.56_{\rm stat}\pm0.13_{\rm syst})\times 10^{-2}$. The $η-η^\prime$ mixing angle in the quark flavor basis is determined to be $ϕ_{\rm P} =(39.8\pm0.8_{\rm stat}\pm0.3_{\rm syst})^\circ$.