First Experimental Constraint on the Scalar Current in the $D^{0(+)} o ar Kll^+ν_{ll}$ 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 $D^{0(+)}\to \bar K\ell^+ν_{\ell}$ 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.

💡 Research Summary

The BESIII Collaboration presents the first experimental constraint on a possible scalar current in the semileptonic charm decays D⁰(⁺) → K̅ℓ⁺ν (ℓ = e, μ). Using a data set of 20.3 fb⁻¹ collected at a centre‑of‑mass energy of √s = 3.773 GeV, where ψ(3770) decays almost exclusively into D⁰\bar D⁰ and D⁺D⁻ pairs, the analysis employs a double‑tag technique to fully reconstruct one D meson and identify the signal decay of the opposite‑side D. The neutrino is inferred from missing mass and energy constraints.

Two observables are measured in bins of the momentum‑transfer squared (q²): (1) the partial decay rates ΔΓ_i, obtained from the yields after efficiency correction, and (2) the forward‑backward asymmetry A_FB(q²) = (N_F – N_B)/(N_F + N_B) for the muon mode, where N_F (N_B) counts events with the charged lepton emitted in the forward (backward) hemisphere relative to the D‑meson direction in the D rest frame. In the Standard Model (SM) the asymmetry is essentially zero for both lepton flavours; a non‑zero scalar contribution would generate a characteristic q²‑dependent A_FB in the μ channel.

Theoretical description is based on an effective‑field‑theory (EFT) extension of the SM weak Hamiltonian that adds a scalar operator O_S = (\bar s c)(\bar ℓ ν) with a dimensionless Wilson coefficient c_S^ℓ. The differential decay width reads

dΓ/dq² = (G_F²|V_cs|²/24π³) p_K³ |f_+(q²)|² (1 + m_ℓ²/2q²) + (G_F²|V_cs|²/8π³) p_K m_ℓ² |f_0(q²)|² |c_S^ℓ|²,

and the forward‑backward asymmetry receives an interference term proportional to Re(c_S^ℓ). The vector form factor f_+(q²) and scalar form factor f_0(q²) are taken from recent lattice‑QCD calculations together with a BCL (Bourrely‑Caprini‑Lellouch) parameterisation; the normalisation f_+(0)·|V_cs| is left as a free parameter in the fit.

A simultaneous χ² fit to the measured ΔΓ_i (both e and μ modes) and A_FB(q²) (μ mode only) extracts Re(c_S^μ), Im(c_S^μ), |V_cs|·f_+(0) and the BCL coefficients. Systematic uncertainties are evaluated by varying tracking and PID efficiencies, background shapes, q² resolution, and the form‑factor model; they are added in quadrature to the statistical errors.

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 result deviates from the SM expectation (c_S^μ = 0) by 1.9 σ, indicating no statistically significant evidence for a scalar contribution but providing the first quantitative bound. The sign ambiguity of the imaginary part reflects the current inability to resolve a possible CP‑violating phase.

In addition to the scalar‑current analysis, the paper reports improved measurements of the absolute branching fractions:

B(D⁰ → K⁻ e⁺ ν) = (3.505 ± 0.014) %,
B(D⁺ → K̅⁰ e⁺ ν) = (8.83 ± 0.04) %.

From the fit, f_+(0)·|V_cs| = 0.718 ± 0.004 is obtained. Using the lattice‑QCD value for f_+(0) (≈0.736), the CKM element is extracted as |V_cs| = 0.973 ± 0.008, consistent with the world average but with a reduced uncertainty.

Lepton‑flavour universality (LFU) is tested by forming the ratios R_{μ/e}(q²) = Γ(D → K μ⁺ ν)/Γ(D → K e⁺ ν) over the full q² range and in two sub‑ranges (0–0.5 GeV² and 0.5–1.0 GeV²). All measured ratios are compatible with the SM prediction of ≈0.975, providing no indication of LFU violation in charm semileptonic decays.

Overall, this work establishes the first experimental limits on scalar currents in D → Kℓν transitions, improves the precision of |V_cs| and the hadronic form factor, and confirms LFU at the few‑percent level. The methodology—simultaneous use of partial rates and forward‑backward asymmetries—sets a benchmark for future high‑statistics charm experiments (e.g., Belle II, LHCb Upgrade) and for global EFT fits that aim to uncover possible new‑physics contributions in the up‑type quark sector.