Precise measurement of the form factors in $D^0\to K^{\ast }(892{)}^{-}\hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼$ and test of lepton universality with $D^0\to K^{\ast }(892{)}^{-}{\ell }^{+}\hat{I}{½}_{\ell }$ decays

Abstract

We report a study of the semileptonic decay $D^0\to {\bar{K}}^0\ddot{I}{€}^{-}\hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼$ based on a sample of $7.9{\mathrm{fb}}^{-1}$ of $e^{+}{e}^{-}$ annihilation data collected at a center-of-mass energy of 3.773~GeV with the BESIII detector at the BEPCII collider. The branching fraction of the decay is measured for the first time to be $\mathcal{B}(D^0\to {\bar{K}}^0\ddot{I}{€}^{-}\hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼)=(1.373\pm 0.020_{\mathrm{stat}}\pm 0.023_{\mathrm{syst}})\%$, where the first uncertainty is statistical and the second is systematic. Based on the investigation of the decay dynamics, we find that the decay is dominated by the $K^{\ast }(892{)}^{-}$ resonance with the branching fraction measured to be $\mathcal{B}(D^0\to K^{\ast }(892{)}^{-}\hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼)=(1.948\pm 0.033_{\mathrm{stat}}\pm 0.036_{\mathrm{syst}})\%$. We also determine the hadronic form factors for the $D^0\to K^{\ast }(892{)}^{-}\hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼$ decay to be $r_V=V(0)/A_1(0)=1.46\pm 0.11_{\mathrm{stat}}\pm 0.04_{\mathrm{syst}}$, $r_2=A_2(0)/A_1(0)=0.71\pm 0.08_{\mathrm{stat}}\pm 0.03_{\mathrm{syst}}$, and $A_1(0)=0.609\pm 0.008_{\mathrm{stat}}\pm 0.008_{\mathrm{syst}}$, where $V(0)$ is the vector form factor and $A_{1,2}(0)$ are the axial form factors evaluated at $q^2=0$. The $A_1(0)$ is measured for the first time in $D^0\to K^{\ast }(892{)}^{-}\hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼$ decay. Averaging the form-factor parameters that we reported previously in $D^0\to K^{\ast }(892{)}^{-}(\to {\bar{K}}^0\ddot{I}{€}^{-})e^{+}\hat{I}{½}_e$ and $D^0\to K^{\ast }(892{)}^{-}(\to K^{-}\ddot{I}{€}^0)\hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼$ decays, we obtain $r_V=1.456\pm 0.040_{\mathrm{stat}}\pm 0.016_{\mathrm{syst}}$, $r_2=0.715\pm 0.031_{\mathrm{stat}}\pm 0.014_{\mathrm{stat}}$, and $A_1(0)=0.614\pm 0.005_{\mathrm{stat}}\pm 0.004_{\mathrm{syst}}$. This is the most precise determination of the form-factor parameters to date measured in $D\to K^{\ast }(892)$ transition, which provide the most stringent test on various theoretical models.

9 pages, 4 figures