Precise measurement of the form factors in $D^0\to K^{\ast }(892{)}^{-}{\ell }^{+}\hat{I}{½}_{\ell }$ and observation of $D^0\to K_2^{\ast }(1430{)}^{-}{\ell }^{+}\hat{I}{½}_{\ell }$

Abstract

We report a study of the semileptonic decays $D^0\to {\bar{K}}^0\ddot{I}{€}^{-}{\ell }^{+}\hat{I}{½}_{\ell }$ (where $\ell =e,\hat{I}¼$) based on a sample of $20.3{\mathrm{fb}}^{-1}$ of $e^{+}{e}^{-}$ annihilation data collected at a center-of-mass energy of 3.773~GeV with the BESIII detector at the BEPCII collider. Based on an investigation of the decay dynamics in $D^0\to {\bar{K}}^0\ddot{I}{€}^{-}{\ell }^{+}\hat{I}{½}_{\ell }$ decays, a $\mathcal{D}-$wave component of $D^0\to K_2^{\ast }(1430{)}^{-}{\ell }^{+}\hat{I}{½}_{\ell }$ is observed for the first time with a statistical significance of $8.0\ddot{I}ƒ$, in addition to the dominant $K^{\ast }(892{)}^{-}$ and $\mathcal{S}-$wave components. The $\mathcal{D}-$wave component is determined to account for $(0.092\pm 0.028_{\mathrm{stat}}\pm 0.018_{\mathrm{syst}})\%$ of the total decay rate. The branching fractions of the dominant $K^{\ast }(892{)}^{-}$ components are measured as $\mathcal{B}(D^0\to K^{\ast }(892{)}^{-}{e}^{+}\hat{I}{½}_e)=(2.043\pm 0.018_{\mathrm{stat}}\pm 0.012_{\mathrm{syst}})\%$ and $\mathcal{B}(D^0\to K^{\ast }(892{)}^{-}\hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼)=(1.964\pm 0.018_{\mathrm{stat}}\pm 0.012_{\mathrm{syst}})\%$, which are the most precise measurements to date and represent significant improvements over the previous world averages. The hadronic form-factor parameters are measured to be $r_V=V(0)/A_1(0)=1.444\pm 0.026_{\mathrm{stat}}\pm 0.010_{\mathrm{syst}}$, $r_2=A_2(0)/A_1(0)=0.752\pm 0.020_{\mathrm{stat}}\pm 0.004_{\mathrm{syst}}$, and $A_1(0)=0.618\pm 0.002_{\mathrm{stat}}\pm 0.004_{\mathrm{syst}}$, where $V(0)$ is the vector form factor and $A_{1,2}(0)$ are the axial-vector form factors evaluated at $q^2=0$. This is the most precise determination of the form-factor parameters to date measured in a $D\to K^{\ast }(892)$ transition. In addition, we report the first model-independent measurement of the $\mathcal{S}-$wave phase shift in the hadronic ${\bar{K}}^0\ddot{I}{€}^{-}$ system.

11 pages, 6 figures