Study of the $D^0\to K^{-}{\mu }^{+}{\nu }_{\mu }$ Dynamics and Test of Lepton Flavor Universality with $D^0\to K^{-}{\ell }^{+}{\nu }_{\ell }$ Decays

Using $e^{+}{e}^{-}$ annihilation data of $2.93{\mathrm{fb}}^{-1}$ collected at center-of-mass energy $\sqrt{s}=3.773\mathrm{GeV}$ with the BESIII detector, we measure the absolute branching fraction of $D^0\to K^{-}{\mu }^{+}{\nu }_{\mu }$ with significantly improved precision: ${\mathcal{B}}_{D^0\to K^{-}{\mu }^{+}{\nu }_{\mu }}=(3.413\pm 0.019_{\text{stat}}\pm 0.035_{\text{syst}})\%$. Combining with our previous measurement of ${\mathcal{B}}_{D^0\to K^{-}{e}^{+}{\nu }_e}$, the ratio of the two branching fractions is determined to be ${\mathcal{B}}_{D^0\to K^{-}{\mu }^{+}{\nu }_{\mu }}/{\mathcal{B}}_{D^0\to K^{-}{e}^{+}{\nu }_e}=0.974\pm 0.007_{\text{stat}}\pm 0.012_{\text{syst}}$, which agrees with the theoretical expectation of lepton flavor universality within the uncertainty. A study of the ratio of the two branching fractions in different four-momentum transfer regions is also performed, and no evidence for lepton flavor universality violation is found with current statistics. Taking inputs from global fit in the standard model and lattice quantum chromodynamics separately, we determine $f_{+}^K(0)=0.7327\pm 0.0039_{\text{stat}}\pm 0.0030_{\text{syst}}$ and $|V_{cs}|=0.955\pm {0.005}_{\text{stat}}\pm {0.004}_{\text{syst}}\pm {0.024}_{\mathrm{LQCD}}$.

Figure 1

Fits to [(a)–(c)] the $M_{\mathrm{BC}}$ distributions for the three ST modes, and (d) the $U_{\text{miss}}$ distribution for $D^0\to K^{-}{\mu }^{+}{\nu }_{\mu }$ candidates. Dots with error bars are data, solid curves show the fit results, dashed curves show the fitted non-peaking background shapes, the dash-dotted curve in (d) is the peaking background shape of $D^0\to K^{-}{\pi }^{+}{\pi }^0$ and the red arrows in (a)–(c) give the $M_{\mathrm{BC}}$ windows.

Figure 2

(a) Fit to the PDRs, (b) projection to $f_{+}^K(q^2)$ for $D^0\to K^{-}{\mu }^{+}{\nu }_{\mu }$, and (c) the measured ${\mathcal{R}}_{\mu /e}$ in each $q^2$ interval. Dots with error bars are data. Solid curves are the fit, the projection or the ${\mathcal{R}}_{\mu /e}$ expected with the parameters in Ref. [17] where the uncertainty is negligible due to strong correlations in hadronic FFs.