Observation of $D^{+}\to \hat{I}{\cdot }^{\prime }\hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼$ and First Study of $D^{+}\to \hat{I}{\cdot }^{\prime }{\ell }^{+}\hat{I}{½}_{\ell }$ Decay Dynamics

Abstract

Using $20.3\mathrm{f}{\mathrm{b}}^{-1}$ 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 $D^{+}\to \hat{I}{\cdot }^{\prime }\hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼$ with significance of $8.6\ddot{I}ƒ$ including systematic uncertainties, and an improved measurement of $D^{+}\to \hat{I}{\cdot }^{\prime }{e}^{+}\hat{I}{½}_e$. The branching fractions of $D^{+}\to \hat{I}{\cdot }^{\prime }\hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼$ and $D^{+}\to \hat{I}{\cdot }^{\prime }{e}^{+}\hat{I}{½}_e$ are determined to be $(1.92\pm 0.28_{\mathrm{stat}}\pm 0.08_{\mathrm{syst}})\times 10^{-4}$ and $(1.79\pm 0.19_{\mathrm{stat}}\pm 0.07_{\mathrm{syst}})\times 10^{-4}$, respectively. The ratio of the two branching fractions is determined to be ${\mathcal{R}}_{\hat{I}¼/e}=1.07\pm 0.19_{\mathrm{stat}}\pm 0.03_{\mathrm{syst}}$, which agrees with the theoretical expectation of lepton flavor universality within the Standard Model.From an analysis of the $D^{+}\to \hat{I}{\cdot }^{\prime }{\ell }^{+}\hat{I}{½}_{\ell }$ decay dynamics, the product of the hadronic form factor $f_{+}^{\hat{I}{\cdot }^{\prime }}(0)$ and the CKM matrix element $|V_{cd}|$ is measured for the first time, giving $f_{+}^{\hat{I}{\cdot }^{\prime }}(0)|V_{cd}|=(5.92\pm 0.56_{\mathrm{stat}}\pm 0.13_{\mathrm{syst}})\times 10^{-2}$. The $\hat{I}\cdot -\hat{I}{\cdot }^{\prime }$ mixing angle in the quark flavor basis is determined to be $\ddot{I}{•}_{\mathrm{P}}=(39.8\pm 0.8_{\mathrm{stat}}\pm 0.3_{\mathrm{syst}}{)}^{\circ }$.