Test of lepton universality and measurement of the form factors of $D^0\to K^{*}(892)^-\mu^+\nu_\mu$

Abstract

We report a first study of the semileptonic decay $D^0\rightarrow K^-\pi^0\mu^{+}\nu_{\mu}$ by analyzing an $e^+e^-$ annihilation data sample of $7.9~\mathrm{fb}^{-1}$ collected at the center-of-mass energy of 3.773 GeV with the BESIII detector. The absolute branching fraction of $D^0\to K^-\pi^0\mu^{+}\nu_{\mu}$ is measured for the first time to be $(0.729 \pm 0.014_{\rm stat} \pm 0.011_{\rm syst})\%$. Based on an amplitude analysis, the $S\text{-}{\rm wave}$ contribution is determined to be $(5.76 \pm 0.35_{\rm stat} \pm 0.29_{\rm syst})\%$ of the total decay rate in addition to the dominated $K^{*}(892)^-$ component. The branching fraction of $D^0\to K^{*}(892)^-\mu^+\nu_\mu$ is given to be $(2.062 \pm 0.039_{\rm stat} \pm 0.032_{\rm syst})\%$, which improves the precision of the world average by a factor of 5. Combining with the world average of ${\mathcal B}(D^0\to K^{*}(892)^-e^+\nu_e)$, the ratio of the branching fractions obtained is $\frac{{\mathcal B}(D^0\to K^{*}(892)^-\mu^+\nu_\mu)}{{\mathcal B}(D^0\to K^{*}(892)^-e^+\nu_e)} = 0.96\pm0.08$, in agreement with lepton flavor universality. Furthermore, assuming single-pole dominance parameterization, the most precise hadronic form factor ratios for $D^0\to K^{*}(892)^{-} \mu^+\nu_\mu$ are extracted to be $r_{V}=V(0)/A_1(0)=1.37 \pm 0.09_{\rm stat} \pm 0.03_{\rm syst}$ and $r_{2}=A_2(0)/A_1(0)=0.76 \pm 0.06_{\rm stat} \pm 0.02_{\rm syst}$.