First Amplitude Analysis of $D^0\rightarrow K^-\pi^0e^+\nu_e$ and Observation of $D^0\rightarrow K^*_2(1430)^-e^+\nu_e$

Abstract

We present the first amplitude analysis of the semileptonic decay $D^0\to K^-\pi^0 e^{+}\nu_{e}$ 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 $K^*_2(1430)^-$ accounting for $(0.16 \pm 0.05_{\rm stat} \pm 0.02_{\rm syst})\%$ of the $K^-\pi^0$ is observed for the first time with a significance of $7.9\sigma$ in addition to the dominant $\mathcal{P}$-wave component of $K^*(892)^-$ and the sub-dominant $K^-\pi^0$ $\mathcal{S}$-wave. The hadronic form factors of the $D^0 \to K^*(892)^-$ transition are measured precisely as $r_V=V(0)/A_1(0)=1.41 \pm 0.05_{\rm stat} \pm 0.01_{\rm syst}$ and $r_2=A_2(0)/A_1(0)=0.77 \pm 0.04_{\rm stat} \pm 0.02_{\rm syst}$. The branching fraction of $D^0\to K^*(892)^-e^+\nu_e$ with $K^*(892)^-\to K^-\pi^0$ is measured to be $(7.403\pm0.061_{\rm stat.} \pm 0.048_{\rm syst.})\times10^{-3}$. Combining the measurements of the $D^0\to K^*(892)^-(K^*(892)^-\to K^-\pi^0)\ell^+ \nu_\ell$, lepton flavor universality is tested by the ratio $\mathcal{R}_{\rm LFU}=\mathcal{B}(D^0\to K^*(892)^-\mu^+ \nu_\mu)/\mathcal{B}(D^0\to K^*(892)^-e^+\nu_e)=0.928\pm0.020_{\rm stat}\pm0.012_{\rm syst}$ with unprecedented precision; no violation is found. Furthermore, isospin symmetry in the decay $K^*(892) \to K\pi$ is tested by $\mathcal R_{K^{*-}} =\mathcal{B}(K^*(892)^-\to K^- \pi^0)/\mathcal{B}(K^*(892)^-\to K_S^0 \pi^-)= 1.09\pm0.02_{\rm stat}\pm0.02_{\rm syst}$ for the first time using the previous measurement of $D^0\to K^*(892)^-e^+\nu_e$ with $K^*(892)^-\to K^0_S\pi^-$. Finally, the phase shift of the $K\pi$ \wv{S} is extracted in a model-independent way, which sheds light on the nature of the lightest strange scalar meson, the $K^*_0(700)$.