# 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

11 January 2019

Abstract: Using ${e}^{+}{e}^{-}$ annihilation data of $2.93\text{}\text{}{\mathrm{fb}}^{-1}$ collected at center-of-mass energy $\sqrt{s}=3.773\text{}\text{}\mathrm{GeV}$ with the BESIII detector, we measure the absolute branching fraction of ${D}^{0}\to {K}^{-}{\mu }^{+}{\nu }_{\mu }$ with significantly improved precision: ${B}_{{D}^{0}\to {K}^{-}{\mu }^{+}{\nu }_{\mu }}=\left(3.413±0.01{9}_{\text{stat}}±0.03{5}_{\text{syst}}\right)%$. Combining with our previous measurement of ${B}_{{D}^{0}\to {K}^{-}{e}^{+}{\nu }_{e}}$, the ratio of the two branching fractions is determined to be ${B}_{{D}^{0}\to {K}^{-}{\mu }^{+}{\nu }_{\mu }}/{B}_{{D}^{0}\to {K}^{-}{e}^{+}{\nu }_{e}}=\phantom{\rule{0ex}{0ex}}0.974±0.00{7}_{\text{stat}}±0.01{2}_{\text{syst}}$, 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 ${f}_{+}^{K}\left(0\right)=0.7327±0.003{9}_{\text{stat}}±0.003{0}_{\text{syst}}$ and $|{V}_{cs}|=0.955±{0.005}_{\text{stat}}±{0.004}_{\text{syst}}±{0.024}_{\mathrm{LQCD}}$.

Published in: Physical Review Letters 122 (2019)