Precise measurement of the form factors in $D^0\rightarrow K^*(892)^-\ell^+ν_{\ell}$ and observation of $D^0\rightarrow K_2^*(1430)^-\ell^+ν_{\ell}$

Abstract

We report a study of the semileptonic decays $D^0 \rightarrow \bar{K}^0π^-\ell^+ν_{\ell}$ (where $\ell=e,~μ$) based on a sample of $20.3~\mathrm{fb}^{-1}$ of $e^+e^-$ annihilation data collected at a center-of-mass energy of 3.773~GeV with the BESIII detector at the BEPCII collider. Based on an investigation of the decay dynamics in $D^0 \rightarrow \bar{K}^0π^-\ell^+ν_{\ell}$ decays, a $\mathcal{D}-$wave component of $D^0\rightarrow K_2^*(1430)^-\ell^+ν_{\ell}$ is observed for the first time with a statistical significance of $8.0σ$, in addition to the dominant $K^*(892)^-$ and $\mathcal{S}-$wave components. The $\mathcal{D}-$wave component is determined to account for $(0.092 \pm 0.028_{\rm stat} \pm 0.018_{\rm syst})\%$ of the total decay rate. The branching fractions of the dominant $K^*(892)^-$ components are measured as $\mathcal{B}(D^0\rightarrow K^{*}(892)^-e^+ν_{e}) = (2.043 \pm 0.018_{\rm stat} \pm 0.012_{\rm syst})\%$ and $\mathcal{B}(D^0\rightarrow K^{*}(892)^-μ^+ν_μ) = (1.964 \pm 0.018_{\rm stat} \pm 0.012_{\rm syst})\%$, which are the most precise measurements to date and represent significant improvements over the previous world averages. The hadronic form-factor parameters are measured to be $r_{V} = V(0)/A_1(0) = 1.444 \pm 0.026_{\rm stat} \pm 0.010_{\rm syst}$, $r_{2} = A_2(0)/A_1(0) = 0.752 \pm 0.020_{\rm stat} \pm 0.004_{\rm syst}$, and $A_1(0)=0.618\pm0.002_{\rm stat} \pm0.004_{\rm syst}$, where $V(0)$ is the vector form factor and $A_{1,2}(0)$ are the axial-vector form factors evaluated at $q^2=0$. This is the most precise determination of the form-factor parameters to date measured in a $D\rightarrow K^*(892)$ transition. In addition, we report the first model-independent measurement of the $\mathcal{S}-$wave phase shift in the hadronic $\bar{K}^0π^-$ system.

Figures (6)

• Figure 1: (Color online) The $M_{\rm BC}$ distributions of the three ST modes. The points are data, the solid blue curves are the total fits and the dashed red curves show the background shapes.
• Figure 2: (Color online) Fits to $U_{\rm miss}$ distributions for the SL decays (left) $D^0\rightarrow \bar{K}^{0}\pi^- e^+\nu_{e}$ and (right) $D^0\rightarrow \bar{K}^{0}\pi^- \mu^+\nu_{\mu}$.
• Figure 3: (Color online) Projections of the fits and data for (a, a$^{\prime}$) $M_{\bar{K}^0\pi^-}$, (b, b$^{\prime}$) $q^2$, (c, c$^{\prime}$) $\cos\theta_{\ell^+}$, (d, d$^{\prime}$) $\cos\theta_{\bar{K}^0}$, and (e, e$^{\prime}$) $\chi$ for the SL decay $D^0\rightarrow \bar{K}^0\pi^-\ell^+\nu_{\ell}$, where the dashed green and dashed pink curves show the contribution of the $\mathcal{S}-$wave and $\mathcal{D}-$wave components. The dots with error bars are data, the red histograms are the fit results, and the shaded histograms are the simulated background.
• Figure 4: (Color online) Comparisons of the $\mathcal{S}-$wave phase shift $\delta_S$ measured in this work with others. The red dots with error bars show the model-independent measurements in this work; the solid red curve shows the result based on the LASS parameterization; the cyan dots, green dots and blue dots show measurements from BESIII prd94_032001, Refs. NPB133_490NPB296_493 and BaBar prd83_072001; The dashed pink curve show the result from BABAR based on the LASS parameterization prd83_072001 with $a^{1/2}_{\rm S,BG}=1.95$ and $b^{1/2}_{\rm S,BG}=1.76$.
• Figure 5: (Color online) Comparisons of the measured $\mathcal{B}(D^0\rightarrow K^{*}(892)^-e^+\nu_{e})$ and $\mathcal{B}(D^0\rightarrow K^{*}(892)^-\mu^+\nu_{\mu})$ with various theoretical calculations from the CQM PRD62_014006PRD96_016017, HM$\chi$T PRD72_034029, LCSR IJMPA21_6125, LCSR 2 PRR2, LCSR 3 2505.01329, CLFQM JPG39_025005EPJC77_587, CCQM FrontPhys14_64401, RQM prd101_013004, $\chi$UA PRD92_054038, and PDG averaged results pdg24. The correlation coefficient between the measured BFs is $0.24$. The color coding for the measured results are the same as in Fig. \ref{['fig:cmpformfactor']}.