Observation of $ {D}^{+}\to {\eta }^{\prime }{\mu }^{+}{\nu }_{\mu }$ and First Experimental Study of $ {D}^{+}\to {\eta }^{\prime }{\ell }^{+}{\nu }_{\ell }$ Decay Dynamics

Using $ 20.3\text{}\text{}{\mathrm{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 {\eta }^{\prime }{\mu }^{+}{\nu }_{\mu }$ with significance of $ 8.6\sigma $ including systematic uncertainties, and an improved measurement of $ {D}^{+}\to {\eta }^{\prime }{e}^{+}{\nu }_{e}$. The branching fractions of $ {D}^{+}\to {\eta }^{\prime }{\mu }^{+}{\nu }_{\mu }$ and $ {D}^{+}\to {\eta }^{\prime }{e}^{+}{\nu }_{e}$ are determined to be $ (1.92\pm 0.2{8}_{\mathrm{stat}}\pm 0.0{8}_{\mathrm{syst}})\times {10}^{-4}$ and $ (1.79\pm 0.1{9}_{\mathrm{stat}}\pm 0.0{7}_{\mathrm{syst}})\times {10}^{-4}$, respectively. The ratio of the two branching fractions is determined to be $ {\mathcal{R}}_{\mu /e}=1.07\pm 0.1{9}_{\mathrm{stat}}\pm 0.0{3}_{\mathrm{syst}}$, which agrees with the theoretical expectation of lepton flavor universality within the standard model. From an analysis of the $ {D}^{+}\to {\eta }^{\prime }{\ell }^{+}{\nu }_{\ell }$ decay dynamics, the product of the hadronic form factor $ {f}_{+}^{{\eta }^{\prime }}(0)$ and the Cabibbo-Kobayashi-Maskawa matrix element $ |{V}_{cd}|$ is measured for the first time, giving $ {f}_{+}^{{\eta }^{\prime }}(0)|{V}_{cd}|=(5.92\pm 0.5{6}_{\mathrm{stat}}\pm 0.1{3}_{\mathrm{syst}})\times {10}^{-2}$. The $ \eta -{\eta }^{\prime }$ mixing angle in the quark flavor basis is determined to be $ {\varphi }_{\mathrm{P}}=(39.8\pm {0.8}_{\mathrm{stat}}\pm {0.3}_{\mathrm{syst}})°$.