Precise measurement of the form factors in $D^0\rightarrow K^*(892)^-\mu^+\nu_{\mu}$ and test of lepton universality with $D^0\rightarrow K^*(892)^-\ell^+\nu_{\ell}$ decays

Abstract

We report a study of the semileptonic decay $D^0 \rightarrow \bar{K}^0\pi^-\mu^+\nu_{\mu}$ based on a sample of $7.9~\mathrm{fb}^{-1}$ of $e^+e^-$ annihilation data collected at a center-of-mass energy of 3.773~GeV with the BESIII detector at the BEPCII collider. The branching fraction of the decay is measured for the first time to be $\mathcal{B}(D^0\rightarrow \bar{K}^0\pi^-\mu^+\nu_{\mu}) = (1.373 \pm 0.020_{\rm stat} \pm 0.023_{\rm syst})\%$, where the first uncertainty is statistical and the second is systematic. Based on the investigation of the decay dynamics, we find that the decay is dominated by the $K^{*}(892)^-$ resonance with the branching fraction measured to be $\mathcal{B}(D^0\rightarrow K^{*}(892)^-\mu^+\nu_{\mu}) = (1.948 \pm 0.033_{\rm stat} \pm 0.036_{\rm syst})\%$. We also determine the hadronic form factors for the $D^0\rightarrow K^{*}(892)^-\mu^+\nu_{\mu}$ decay to be $r_{V} = V(0)/A_1(0) = 1.46 \pm 0.11_{\rm stat} \pm 0.04_{\rm syst}$, $r_{2} = A_2(0)/A_1(0) = 0.71 \pm 0.08_{\rm stat} \pm 0.03_{\rm syst}$, and $A_1(0)=0.609 \pm 0.008_{\rm stat} \pm 0.008_{\rm syst}$, where $V(0)$ is the vector form factor and $A_{1,2}(0)$ are the axial form factors evaluated at $q^2=0$. The $A_1(0)$ is measured for the first time in $D^0\rightarrow K^{*}(892)^-\mu^+\nu_{\mu}$ decay. Averaging the form-factor parameters that we reported previously in $D^0\rightarrow K^*(892)^-(\rightarrow \bar{K}^0\pi^-)e^+\nu_{e}$ and $D^0\rightarrow K^*(892)^-(\rightarrow K^-\pi^0)\mu^+\nu_{\mu}$ decays, we obtain $r_{V}=1.456\pm0.040_{\rm stat}\pm0.016_{\rm syst}$, $r_{2}=0.715\pm0.031_{\rm stat}\pm0.014_{\rm stat}$, and $A_1(0)=0.614\pm0.005_{\rm stat}\pm0.004_{\rm syst}$. This is the most precise determination of the form-factor parameters to date measured in $D\rightarrow K^*(892)$ transition, which provide the most stringent test on various theoretical models.