Kavli Affiliate: Chris Xu
| First 5 Authors: BESIII Collaboration, BESIII Collaboration, , ,

| Summary:
We report the first measurement of the semileptonic decay $D^+_s rightarrow K^0μ^+ν_μ$, using a sample of $e^+e^-$ annihilation data corresponding to an integrated luminosity of $7.33~mathrmfb^-1$ 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 $mathcalB(D^+_srightarrow K^0μ^+ν_μ) = (2.89 pm 0.27_rm stat pm 0.12_rm syst)times 10^-3$, 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 $D^+_s rightarrow K^0μ^+ν_μ$ and $D^+_s rightarrow K^0e^+ν_e$ 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 $f^K^0_+(0)|V_cd|=0.140pm0.008_rm statpm0.002_rm syst$. Using $|V_cd|=0.22486pm0.00068$ as an input, the hadronic form factor is determined to be $f^K^0_+(0)=0.623pm0.036_rm stat pm 0.009_rm syst$ 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 $f^K^0_+(0)=0.6307pm0.0020$ from lattice calculations as an input, we obtain $|V_cd|=0.220pm0.013_rm statpm0.003_rm systpm0.001_rm LQCD$, which is the most precise determination of $|V_cd|$ using the $D_s^+rightarrow K^0ell^+ν_ell$ decays. In addition, lepton flavor universality is tested for the first time with $D^+_s rightarrow K^0ell^+ν_ell$ decays in full and separate $q^2$ intervals. No obvious violation is found.
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