We report the first measurement of the semileptonic decay $D^+_s \rightarrow K^0\mu^+\nu_{ \mu}$, using a sample of $e^+e^-$ annihilation data corresponding to an integrated luminosity of $7.33~\mathrm{ fb}^{ -1}$ collected at center-of-mass energies between 4.128 to 4.226~GeV with the BESIII detector at the BEPCII collider. The branching fraction of the decay is measured to be $\mathcal{ B}(D^+_s\rightarrow K^0\mu^+\nu_{ \mu}) = (2.89 \pm 0.27_{ \rm stat} \pm 0.12_{ \rm syst})\times 10^{ -3}$, where the first uncertainty is statistical and the second is systematic. Based on a simultaneous fit to the partial decay rates in $q^2$ intervals measured in $D^+_s \rightarrow K^0\mu^+\nu_{ \mu}$ and $D^+_s \rightarrow K^0e^+\nu_{ e}$ decays, the product value of the form factor $f^{ K^0}_{ +}(0)$ and the Cabibbo-Kobayashi-Maskawa matrix element $|V_{ cd}|$ is measured to be $f^{ K^0}_{ +}(0)|V_{ cd}|=0.140\pm0.008_{ \rm stat}\pm0.002_{ \rm syst}$. Using $|V_{ cd}|=0.22486\pm0.00068$ as an input, the hadronic form factor is determined to be $f^{ K^0}_{ +}(0)=0.623\pm0.036_{ \rm stat} \pm 0.009_{ \rm syst}$ at $q^2=0$. This is the most precise determination of $f^{ K^0}_{ +}(0)$ in the $D^+_s \rightarrow K^0$ transition to date. The measured branching fraction and form factor presented in this work provide the most stringent test on various non-perturbative theoretical calculations. Taking $f^{ K^0}_{ +}(0)=0.6307\pm0.0020$ from lattice calculations as an input, we obtain $|V_{ cd}|=0.220\pm0.013_{ \rm stat}\pm0.003_{ \rm syst}\pm0.001_{ \rm LQCD}$, which is the most precise determination of $|V_{ cd}|$ using the $D_s^+\rightarrow K^0\ell^+\nu_{ \ell}$ decays. In addition, lepton flavor universality is tested for the first time with $D^+_s \rightarrow K^0\ell^+\nu_{ \ell}$ decays in full and separate $q^2$ intervals. No obvious violation is found.
Categories: hep-ex