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

Abstract

We present the first amplitude analysis of the semileptonic decay $D^0\to K^-π^0 e^{+}ν_{e}$ 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 $K^-π^0$ is observed for the first time with a significance of $7.9σ$ in addition to the dominant $\mathcal{P}$-wave component of $K^*(892)^-$ and the sub-dominant $K^-π^0$ $\mathcal{S}$-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 $D^0\to K^*(892)^-e^+ν_e$ with $K^*(892)^-\to K^-π^0$ is measured to be $(7.403\pm0.061_{\rm stat.} \pm 0.048_{\rm syst.})\times10^{-3}$. Combining the measurements of the $D^0\to K^*(892)^-(K^*(892)^-\to K^-π^0)\ell^+ ν_\ell$, lepton flavor universality is tested by the ratio $\mathcal{R}_{\rm LFU}=\mathcal{B}(D^0\to K^*(892)^-μ^+ ν_μ)/\mathcal{B}(D^0\to K^*(892)^-e^+ν_e)=0.928\pm0.020_{\rm stat}\pm0.012_{\rm syst}$ with unprecedented precision; no violation is found. Furthermore, isospin symmetry in the decay $K^*(892) \to Kπ$ is tested by $\mathcal R_{K^{*-}} =\mathcal{B}(K^*(892)^-\to K^- π^0)/\mathcal{B}(K^*(892)^-\to K_S^0 π^-)= 1.09\pm0.02_{\rm stat}\pm0.02_{\rm syst}$ for the first time using the previous measurement of $D^0\to K^*(892)^-e^+ν_e$ with $K^*(892)^-\to K^0_Sπ^-$. Finally, the phase shift of the $Kπ$ \wv{S} is extracted in a model-independent way, which sheds light on the nature of the lightest strange scalar meson, the $K^*_0(700)$.

Figures (3)

• Figure 1: The data and fits for $U_{\rm miss}$ and the projections onto the five kinematic variables of $D^0\to K^-\pi^0 e^+\nu_e$ decay; The dots with error bars represent the data, the blue curves indicate the total fit, and the filled gray histograms show the background contributions. The dashed violet, dashed red, and dash-dotted orange lines correspond to the $\mathcal{S}$, $\mathcal{P}$, and $\mathcal{D}$-wave components, respectively. Here ${\rm Nbin}$ denotes the number of bins. For the $\chi^2/$Nbin calculation, we merge neighboring bins with very few entries until at least 20 entries are accumulated.
• Figure 2: $\mathcal{S}$-wave phase (left) and magnitude (right) versus $m_{K ^-\pi^0}$, assuming that the signal is composed of the $\mathcal{S}$, $\mathcal{P}$$\left({K}^{*}(892)^-\right)$ and $\mathcal{D}$-wave $\left({K}_2^*(1430)^-\right)$. The dots with error bars represent the fit results from the model-independent measurement, and the black solid line corresponds to the nominal solution based on Table \ref{['tab:ff-sum']}, while the dashed lines reflect the propagated $\pm 1\sigma$ uncertainties.
• Figure 3: Comparison of the measured FFs, PDG values and theoretical predictions from Refs. HMChiT2005CLFQM2012ABADA2003625CCQM2019CQM2017CQM2000LCSR2006LCSR2020RQM2020CLFQM2012CLFQM2017LEChiQM2014RQM2020HQCD2024HQEFT2003. The inner, middle, and outer ellipses correspond to uncertainty ranges of $1\sigma$, $2\sigma$ and $3\sigma$ deviations, respectively.