First Amplitude Analysis of $D^0\to K^{-}\ddot{I}{€}^0{e}^{+}\hat{I}{½}_e$ and Observation of $D^0\to K_2^{\ast }(1430{)}^{-}{e}^{+}\hat{I}{½}_e$

Abstract

We present the first amplitude analysis of the semileptonic decay $D^0\to K^{-}\ddot{I}{€}^0{e}^{+}\hat{I}{½}_e$ by analyzing $e^{+}{e}^{-}$ annihilation data corresponding to an integrated luminosity of 20.3 fb${}^{-1}$ collected at the center-of-mass energy of 3.773 GeV with the BESIII detector. A tiny $\mathcal{D}$-wave component of the $K_2^{\ast }(1430{)}^{-}$ accounting for $(0.16\pm 0.05_{\mathrm{stat}}\pm 0.02_{\mathrm{syst}})\%$ of the $K^{-}\ddot{I}{€}^0$ is observed for the first time with a significance of $7.9\ddot{I}ƒ$ in addition to the dominant $\mathcal{P}$-wave component of $K^{\ast }(892{)}^{-}$ and the sub-dominant $K^{-}\ddot{I}{€}^0$ $\mathcal{S}$-wave. The hadronic form factors of the $D^0\to K^{\ast }(892{)}^{-}$ transition are measured precisely as $r_V=V(0)/A_1(0)=1.41\pm 0.05_{\mathrm{stat}}\pm 0.01_{\mathrm{syst}}$ and $r_2=A_2(0)/A_1(0)=0.77\pm 0.04_{\mathrm{stat}}\pm 0.02_{\mathrm{syst}}$. The branching fraction of $D^0\to K^{\ast }(892{)}^{-}{e}^{+}\hat{I}{½}_e$ with $K^{\ast }(892{)}^{-}\to K^{-}\ddot{I}{€}^0$ is measured to be $(7.403\pm 0.061_{stat.}\pm 0.048_{syst.})\times 10^{-3}$. Combining the measurements of the $D^0\to K^{\ast }(892{)}^{-}(K^{\ast }(892{)}^{-}\to K^{-}\ddot{I}{€}^0){\ell }^{+}\hat{I}{½}_{\ell }$, lepton flavor universality is tested by the ratio ${\mathcal{R}}_{\mathrm{LFU}}=\mathcal{B}(D^0\to K^{\ast }(892{)}^{-}\hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼)/\mathcal{B}(D^0\to K^{\ast }(892{)}^{-}{e}^{+}\hat{I}{½}_e)=0.928\pm 0.020_{\mathrm{stat}}\pm 0.012_{\mathrm{syst}}$ with unprecedented precision; no violation is found. Furthermore, isospin symmetry in the decay $K^{\ast }(892)\to K\ddot{I}€$ is tested by ${\mathcal{R}}_{K^{\ast -}}=\mathcal{B}(K^{\ast }(892{)}^{-}\to K^{-}\ddot{I}{€}^0)/\mathcal{B}(K^{\ast }(892{)}^{-}\to K_S^0\ddot{I}{€}^{-})=1.09\pm 0.02_{\mathrm{stat}}\pm 0.02_{\mathrm{syst}}$ for the first time using the previous measurement of $D^0\to K^{\ast }(892{)}^{-}{e}^{+}\hat{I}{½}_e$ with $K^{\ast }(892{)}^{-}\to K_S^0\ddot{I}{€}^{-}$. Finally, the phase shift of the $K\ddot{I}€$ \wv{S} is extracted in a model-independent way, which sheds light on the nature of the lightest strange scalar meson, the $K_0^{\ast }(700)$.

9 pages, 3 figures