First Measurement of the $D_s^+\rightarrow K^0μ^+ν_μ$ Decay

Abstract

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 $7.33~\mathrm{fb}^{-1}$ 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 $\mathcal{B}(D^+_s\rightarrow K^0μ^+ν_μ) = (2.89 \pm 0.27_{\rm stat} \pm 0.12_{\rm syst})\times 10^{-3}$, 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 $f^{K^0}_{+}(0)|V_{cd}|=0.140\pm0.008_{\rm stat}\pm0.002_{\rm syst}$. 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 $D_s^+\rightarrow K^0\ell^+ν_{\ell}$ decays. In addition, lepton flavor universality is tested for the first time with $D^+_s \rightarrow K^0\ell^+ν_{\ell}$ decays in full and separate $q^2$ intervals. No obvious violation is found.

Figures (6)

• Figure 1: (Color online) Fits to $M_{D_s^-}$ distributions for the fourteen tag modes. Points with error bars are data, blue dashed curves are the fitted backgrounds and red solid curves are the total fits.
• Figure 2: (Color online) Fits to the ${\rm MM}^2$ distribution of SL candidate events. Dots with error bars are data, dot-dashed lines (blue) are the fitted combinatorial backgrounds and solid curves (red) are the total fits. The long-dashed lines (pink) show the fitted background from $D^+_s\rightarrow K^0\pi^+\pi^0$.
• Figure 3: (Color online) Fits to the partial decay rates for (a) $D_s^+\rightarrow K^0e^+\nu_e$ and (b) $D_s^+\rightarrow K^0\mu^+\nu_{\mu}$. (c) Projection onto $f^{K^0}_+(q^2)$ for the two SL decays, while the hatched curves show the LQCD prediction in Ref. PRD107_094516. (d) The measured $\mathcal{R}^{\mu/e}_{K^0}(q^2)$ in various $q^2$ intervals. Dots with error bars are data, the curves show the fits with various FF parameterizations.
• Figure 4: (Color online) (Upper) Comparisons of $f^{K^0}_+(q^2)$ measured in this work with those calculated from the LQCD PRD107_094516, CQM PRD62_014006, LCSR$_1$IJMPA21_6125, LCSR$_2$plb857_138975, CLFQM JPG39_025005, CCQM PRD98_114031, RQM prd101_013004, and the hQCD prd109_026008. (Bottom) Distribution of $\chi=[f^{\rm meas}_+(q^2)-f^{\rm LQCD}_+(q^2)]/[\sqrt{\sigma^2_{f^{\rm meas}_+(q^2)}+\sigma^2_{f^{\rm LQCD}_+(q^2)}}]$, calculated with the measured FFs and predicted FFs of the LQCD PRD107_094516.
• Figure 5: (Color online) Comparisons of measured BFs for $D^+_s\rightarrow K^{0} e^+\nu_{e}$prd110_052012 and $D^+_s\rightarrow K^{0}\mu^+\nu_{\mu}$ with various theoretical calculations from the CQM PRD62_014006, LCSR$_1$IJMPA21_6125, LCSR$_2$plb857_138975, HM$\chi$T PRD71_014020, CLFQM$_1$PRD78_054002, CLFQM$_2$JPG39_025005EPJC77_587, CCQM FrontPhys14_64401PRD98_114031, and RQM prd101_013004. The correlation coefficient between the measured BFs is 0.07.