First Observation of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup><mml:mo stretchy="false">→</mml:mo><mml:mi>η</mml:mi><mml:msup><mml:mrow><mml:mi>μ</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup><mml:msub><mml:mrow><mml:mi>ν</mml:mi></mml:mrow><mml:mrow><mml:mi>μ</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math> and Measurement of Its Decay Dynamics

By analyzing a data sample corresponding to an integrated luminosity of 2.93 fb^{-1} collected at a center-of-mass energy of 3.773 GeV with the BESIII detector, we measure for the first time the absolute branching fraction of the D^{+}→ημ^{+}ν_{μ} decay to be B_{D^{+}→ημ^{+}ν_{μ}}=(10.4±1.0_{stat}±0.5_{syst})×10^{-4}. Using the world averaged value of B_{D^{+}→ηe^{+}ν_{e}}, the ratio of the two branching fractions is determined to be B_{D^{+}→ημ^{+}ν_{μ}}/B_{D^{+}→ηe^{+}ν_{e}}=0.91±0.13_{(stat+syst)}, which agrees with the theoretical expectation of lepton flavor universality within uncertainty. By studying the differential decay rates in five four-momentum transfer intervals, we obtain the product of the hadronic form factor f_{+}^{η}(0) and the c→d Cabibbo-Kobayashi-Maskawa matrix element |V_{cd}| to be f_{+}^{η}(0)|V_{cd}|=0.087±0.008_{stat}±0.002_{syst}. Taking the input of |V_{cd}| from the global fit in the standard model, we determine f_{+}^{η}(0)=0.39±0.04_{stat}±0.01_{syst}. On the other hand, using the value of f_{+}^{η}(0) calculated in theory, we find |V_{cd}|=0.242±0.022_{stat}±0.006_{syst}±0.033_{theory}.