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

Abstract

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 $D^{0(+)}\to \bar K\ell^+ν_{\ell}$ 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 ${\rm Re}(c_S^μ)=0.007\pm0.008_{\rm stat}\pm0.006_{\rm syst}$ and ${\rm Im}(c_S^μ)=\pm(0.070\pm0.013_{\rm stat}\pm0.010_{\rm syst})$, which deviates from the SM by a significance of $1.9σ$. The branching fractions of $D^{0(+)}\to \bar K\ell^+ν_\ell$, the hadronic form factor $f_+(0)$, and the modulus of the $c\to s$ CKM matrix element $|V_{cs}|$ 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.

Figures (3)

• Figure 1: Fits to the $U_{\rm miss}$ distributions of $D^{0(+)}\to \bar{K}\ell^+\nu_{\ell}$. The points with error bars are data. The blue solid lines denote the total fits. The red, blue, and black dashed lines show the signal, peaking background, and other background contributions, respectively.
• Figure 2: Simultaneous fit to the measured partial decay rates (top) and forward-backward asymmetries (middle) of $D^{0(+)}\to \bar{K}\ell^+\nu_{\ell}$, and the fit projections on the ratios of differential decay rates $\mathcal{R}_{\mu/e}$ (bottom). The black points with red error bars are data, the solid lines are the fit projections with scalar current (SC) contribution included, and the dashed lines are the fit projections without scalar current contribution.
• Figure 3: The confidence regions of (a) the scalar combination of complex Wilson coefficients $c_S^\mu$ with probabilities of 68%, 95%, and 99% from $D^{0(+)}\to \bar{K}\ell^+\nu_{\ell}$, as well as (b)(c) the right- and left-handed real Wilson coefficients $c^\ell_{R}$ and $c^\ell_{L}$ with probabilities of 68% by combining with the $D_s^+\to\ell^+\nu_\ell$ decay rate. The red dot indicates the SM value.