Precise measurements of $D^0 \to K^-\ell^+ν_\ell$ and $D^+ \to \bar K^0\ell^+ν_\ell$ decays

TL;DR

This study provides high-precision determinations of D^0 -> K^-\\ell^+\\nu_ell and D^+ -> \\bar{K}^0\\ell^+\\nu_ell decays using 20.3 fb^{-1} of data from BESIII at 3.773 GeV. Employing a double-tag method and full angular/q^2-based analyses, the work yields absolute branching fractions, partial decay rates, forward-backward asymmetries, and a combined extraction of the hadronic form factor product f_+(0)|V_cs| along with the shape parameter r1(t_0). By combining decay-rate and asymmetry information in a global fit, the paper constrains scalar currents in the c -> s\\ell^+\\nu_ell transition, finding a 1.9σ indication in the muon channel, and provides stringent tests of LFU and CKM unitarity when using LQCD inputs for f_+(0) or |V_cs|. The results offer precise benchmarks for lattice QCD and other theoretical form-factor calculations, and they deepen our understanding of potential new-physics scalar interactions in charm semileptonic decays.

Abstract

Using $e^+e^-$ collision data corresponding to an integrated luminosity of 20.3 fb$^{-1}$, collected at the center-of-mass energy of 3.773 GeV with the BESIII detector, we present precise measurements of $D^0 \to K^-\ell^+ν_\ell$ and $D^+ \to \bar K^0\ell^+ν_\ell$($\ell=e,μ$) decays. The branching fractions of $D^0\to K^-e^+ν_e$, $D^0\to K^-μ^+ν_μ$, $D^+\to \bar K^0e^+ν_e$, and $D^+\to \bar K^0μ^+ν_μ$ are measured to be $(3.527\pm0.005_{\rm stat}\pm0.016_{\rm syst}) \%$, $(3.429\pm0.007_{\rm stat}\pm0.017_{\rm syst}) \%$, $(8.918\pm0.025_{\rm stat}\pm0.050_{\rm syst}) \%$, and $(8.763\pm0.029_{\rm stat}\pm0.052_{\rm syst}) \%$, respectively. The partial decay rates of these four decays are measured with improved precision, and their forward-backward asymmetries are determined for the first time. By performing a simultaneous fit to the measured partial decay rates and the forward-backward asymmetries of $D \to \bar K\ell^+ν_{\ell}$, a search for a possible scalar current contribution in the $c\to s\ell^+ν_{\ell}$ transition is performed. The results are ${\rm Re}(c_S^μ)=0.007\pm0.008_{\rm stat}\pm0.006_{\rm syst}$ and ${\rm Im}(c_S^μ)=\pm(0.070\pm0.013_{\rm stat}\pm0.010_{\rm syst})$, corresponding to a difference from the SM with a significance of $1.9σ$. The product of the form factor $f_+(0)$ and the modulus of the $c\to s$ Cabibbo-Kobayashi-Maskawa matrix element $|V_{cs}|$ is determined to be $f_(0)|V_{cs}|=0.7160\pm0.0007_{\rm stat}\pm0.0014_{\rm syst}$. With the inputs $|V_{cs}|=0.97349\pm0.00016$ from the Standard Model global fit or $f_+(0)=0.7452\pm0.0031$ from the lattice quantum chromodynamics calculation, we derive $f_+(0)=0.7355\pm0.0007_{\rm stat}\pm0.0014_{\rm syst}$ and $|V_{cs}|=0.9608\pm0.0009_{\rm stat}\pm0.0019_{\rm syst}\pm0.0040_{\rm LQCD}$. Lepton flavor universality is also tested.

Figures (17)

• Figure 1: The $M_{\rm BC}$ distributions of the ST $\bar{D}$ candidates in data, with fit results overlaid. The points with error bars are data, the blue curves are the best fits, and the red dashed curves are the fitted ARGUS functions. The pairs of red arrows show the $M_{\rm BC}$ signal windows, and the yellow filled histograms are the combinatorial background from the inclusive MC simulation.
• Figure 2: $U_{\rm miss}$ distributions of the accepted candidate events for $D \to \bar{K}\ell^+\nu_{\ell}$ in data, shown on a logarithmic scale with fit results overlaid. 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 combinatorial background contributions, respectively.
• Figure 3: The $U_{\rm miss}$ distributions of the accepted candidate events for $D^0\to K^-e^+\nu_e$ in individual $q^2$ intervals in data, with fit results overlaid. The points with error bars are data, the blue solid curves are the fit results, the red dashed curves are the signal shapes, and the black dashed curves are the fitted combinatorial background shapes.
• Figure 4: Fits to the partial decay rates of $D \to \bar{K}\ell^+\nu_{\ell}$ and projections of the form factor as functions of $q^2$, where the red points with error bars are the measured partial decay rates and the solid curves are the best fits. The fit qualities are available in Table \ref{['tab:fit_par']}.
• Figure 5: (a)--(b) Simultaneous fit to the partial decay rates of $D^0(D^+)\to \bar{K}\ell^+\nu_\ell$. (c) Hadronic form factor $f_+(q^2)$ as a function of $q^2$ for the four signal modes. (d)--(e) Ratios of differential decay rates of $D^0\to K^-\mu^+\nu_\mu$ over $D^0\to K^-e^+\nu_e$ and $D^+\to \bar{K}^0\mu^+\nu_\mu$ over $D^+\to \bar{K}^0e^+\nu_e$ in each $q^2$ bin, respectively. The dots with error bars are data, and the solid lines are the results with the parameters of the simultaneous fit. The colors red, green, blue, and purple are for $D^0\to K^-e^+\nu_e$, $D^+\to \bar{K}^0e^+\nu_e$, $D^0\to K^-\mu^+\nu_\mu$, and $D^+\to \bar{K}^0\mu^+\nu_\mu$, respectively. The fit quality is available in Table \ref{['tab:fit_par']}.