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

Abstract

We report a first study of the semileptonic decay $D^0\to K^{-}\ddot{I}{€}^0\hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼$ by analyzing an $e^{+}{e}^{-}$ annihilation data sample of $7.9{\mathrm{fb}}^{-1}$ collected at the center-of-mass energy of 3.773 GeV with the BESIII detector. The absolute branching fraction of $D^0\to K^{-}\ddot{I}{€}^0\hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼$ is measured for the first time to be $(0.729\pm 0.014_{\mathrm{stat}}\pm 0.011_{\mathrm{syst}})\%$. Based on an amplitude analysis, the $S\text{-}\mathrm{wave}$ contribution is determined to be $(5.76\pm 0.35_{\mathrm{stat}}\pm 0.29_{\mathrm{syst}})\%$ of the total decay rate in addition to the dominated $K^{\ast }(892{)}^{-}$ component. The branching fraction of $D^0\to K^{\ast }(892{)}^{-}\hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼$ is given to be $(2.062\pm 0.039_{\mathrm{stat}}\pm 0.032_{\mathrm{syst}})\%$, which improves the precision of the world average by a factor of 5. Combining with the world average of $\mathcal{B}(D^0\to K^{\ast }(892{)}^{-}{e}^{+}\hat{I}{½}_e)$, the ratio of the branching fractions obtained is $\frac{\mathcal{B}(D^0\to K^{\ast }(892{)}^{-}\hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼)}{\mathcal{B}(D^0\to K^{\ast }(892{)}^{-}{e}^{+}\hat{I}{½}_e)}=0.96\pm 0.08$, in agreement with lepton flavor universality. Furthermore, assuming single-pole dominance parameterization, the most precise hadronic form factor ratios for $D^0\to K^{\ast }(892{)}^{-}\hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼$ are extracted to be $r_V=V(0)/A_1(0)=1.37\pm 0.09_{\mathrm{stat}}\pm 0.03_{\mathrm{syst}}$ and $r_2=A_2(0)/A_1(0)=0.76\pm 0.06_{\mathrm{stat}}\pm 0.02_{\mathrm{syst}}$.

10 pages, 3 figures