First Measurement of the $D_s^{+}\to K^0\hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼$ Decay

Abstract

We report the first measurement of the semileptonic decay $D_s^{+}\to K^0\hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼$, 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 $\mathcal{B}(D_s^{+}\to K^0\hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼)=(2.89\pm 0.27_{\mathrm{stat}}\pm 0.12_{\mathrm{syst}})\times 10^{-3}$, 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 $D_s^{+}\to K^0\hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼$ and $D_s^{+}\to K^0{e}^{+}\hat{I}{½}_e$ 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 $f_{+}^{K^0}(0)|V_{cd}|=0.140\pm 0.008_{\mathrm{stat}}\pm 0.002_{\mathrm{syst}}$. Using $|V_{cd}|=0.22486\pm 0.00068$ as an input, the hadronic form factor is determined to be $f_{+}^{K^0}(0)=0.623\pm 0.036_{\mathrm{stat}}\pm 0.009_{\mathrm{syst}}$ at $q^2=0$. This is the most precise determination of $f_{+}^{K^0}(0)$ in the $D_s^{+}\to K^0$ 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 $f_{+}^{K^0}(0)=0.6307\pm 0.0020$ from lattice calculations as an input, we obtain $|V_{cd}|=0.220\pm 0.013_{\mathrm{stat}}\pm 0.003_{\mathrm{syst}}\pm 0.001_{\mathrm{LQCD}}$, which is the most precise determination of $|V_{cd}|$ using the $D_s^{+}\to K^0{\ell }^{+}\hat{I}{½}_{\ell }$ decays. In addition, lepton flavor universality is tested for the first time with $D_s^{+}\to K^0{\ell }^{+}\hat{I}{½}_{\ell }$ decays in full and separate $q^2$ intervals. No obvious violation is found.

10 pages, 6 figures