Precise measurements of $D^0 o K^-ll^+ν_ll$ and $D^+ o ar K^0ll^+ν_ll$ decays

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.

💡 Research Summary

The BESIII Collaboration presents a high‑precision study of the semileptonic decays D⁰→K⁻ℓ⁺ν_ℓ and D⁺→K̅⁰ℓ⁺ν_ℓ (ℓ = e, μ) using a data set of 20.3 fb⁻¹ collected at a center‑of‑mass energy of 3.773 GeV, corresponding to the ψ(3770) resonance where D⁰D̅⁰ and D⁺D⁻ pairs are produced copiously. The analysis employs the double‑tag technique: one D meson is fully reconstructed in a hadronic decay mode (the “tag”), and the remaining system is examined for the signal decay. By exploiting energy‑momentum conservation, the missing neutrino four‑momentum is inferred, allowing the determination of the squared momentum transfer q² = (p_ℓ + p_ν)². The q² spectrum is divided into ten bins, and the partial decay rates dΓ/dq² are measured in each bin.

Branching fractions are obtained with unprecedented precision:
• B(D⁰→K⁻e⁺ν_e) = (3.527 ± 0.005_stat ± 0.016_syst) %
• B(D⁰→K⁻μ⁺ν_μ) = (3.429 ± 0.007_stat ± 0.017_syst) %
• B(D⁺→K̅⁰e⁺ν_e) = (8.918 ± 0.025_stat ± 0.050_syst) %
• B(D⁺→K̅⁰μ⁺ν_μ) = (8.763 ± 0.029_stat ± 0.052_syst) %

These measurements improve upon previous world averages by roughly a factor of two in precision. The analysis also extracts the forward‑backward asymmetry A_FB(q²) of the charged lepton, a quantity that is sensitive to scalar contributions in the underlying c→sℓν transition. This is the first experimental determination of A_FB for these modes.

To probe possible scalar currents beyond the Standard Model (SM), the authors perform a simultaneous fit to the measured partial rates and A_FB(q²) using an effective Lagrangian that adds a scalar operator with complex coefficient c_S^μ = Re(c_S^μ) + i Im(c_S^μ). The fit yields
Re(c_S^μ) = 0.007 ± 0.008_stat ± 0.006_syst,
Im(c_S^μ) = ±(0.070 ± 0.013_stat ± 0.010_syst).
The deviation from the SM expectation (c_S^μ = 0) corresponds to a significance of 1.9σ, indicating a mild tension but not yet a definitive sign of new physics.

From the integrated partial rates the product |V_cs|·f₊(0) is determined to be 0.7160 ± 0.0007_stat ± 0.0014_syst. By inserting the CKM matrix element |V_cs| = 0.97349 ± 0.00016 from global fits, the vector form factor at zero momentum transfer is extracted as f₊(0) = 0.7355 ± 0.0015. Conversely, using the lattice QCD (LQCD) calculation f₊(0) = 0.7452 ± 0.0031 yields |V_cs| = 0.9608 ± 0.0045, a value slightly below the SM expectation but compatible within uncertainties.

Lepton flavor universality (LFU) is tested by forming the ratio R_{μ/e} = Γ(D→Kμν)/Γ(D→Keν). The measured ratio, R_{μ/e} = 0.974 ± 0.006_stat ± 0.004_syst, agrees with the SM prediction (≈0.985) at the one‑sigma level, providing no evidence for LFU violation in these decays.

Systematic uncertainties are thoroughly evaluated. Major contributions arise from tracking and PID efficiencies (≈0.3 % each), K⁰_S reconstruction (≈0.4 %), modeling of signal and background shapes, and the knowledge of the beam energy. The total systematic error on the branching fractions is about 0.5 % for the neutral‑D modes and 0.6 % for the charged‑D modes.

In summary, this work delivers the most precise measurements to date of D→Kℓν branching fractions, q²‑dependent partial rates, and forward‑backward asymmetries. It places stringent constraints on possible scalar interactions in charm semileptonic decays and provides an updated determination of the product |V_cs|·f₊(0). While a 1.9σ hint of a scalar contribution is observed, the result is not yet conclusive. Future data sets with larger integrated luminosities, such as those anticipated from the continued BESIII program or a next‑generation Super Tau‑Charm factory, will be essential to either confirm or refute this modest deviation and to further test lepton flavor universality in the charm sector.