First Experimental Constraint on the Scalar Current in the $D^{0(+)}\to \bar{K}{\mathrm{\ell }}^{+}{\nu }_{\mathrm{\ell }}$ Transition

Using 20.3 fb${}^{-1}$ of $e^{+}{e}^{-}$ collision data taken at the center-of-mass energy of $\sqrt{s}=3.773$ GeV, we report the first experimental constraint on the scalar current in the $D^{0(+)}\to \bar{K}{\mathrm{\ell }}^{+}{\nu }_{\mathrm{\ell }}$ transitions, based on a simultaneous fit to the first measured forward-backward asymmetries and precisely determined partial decay rates. The parameters of the scalar current are determined to be $\mathrm{R}\mathrm{e}(c_S^{\mu })=0.007\pm {0.008}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}}\pm {0.006}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}}$ and $\mathrm{I}\mathrm{m}(c_S^{\mu })=\pm (0.070\pm {0.013}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}}\pm {0.010}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}})$, which deviates from the SM by a significance of $1.9\sigma$. The branching fractions of $D^{0(+)}\to \bar{K}{\mathrm{\ell }}^{+}{\nu }_{\mathrm{\ell }}$, the hadronic form factor $f_{+}(0)$, and the modulus of the $c\to s$ CKM matrix element $\mathrm{\mid }{V}_{cs}\mathrm{\mid }$ are also determined with improved precision. In addition, lepton flavor universality is tested via the ratios of the decay rates between semi-muonic and semi-electronic decays in the full momentum transfer range and in subranges.