Prospective analysis of CKM element |Vcd| and D+-meson decay constant from leptonic decays D+ → ℓ+ν

Abstract

The leptonic decay of D+-meson has attracted significant interest due to its unique characteristics. In this paper, we carry out an investigation into the D+-meson leptonic decays D+→ℓ+νℓ with ℓ=(e,μ,τ) by employing the QCD sum rules approach. In which the D+-meson decay constant fD+ is an important input parameter in the process. To enhance the accuracy of our calculations for fD+, we consider the quark propagator and vertex up to dimension-six within the framework of background field theory. Consequently, we obtain the QCD sum rule expression for fD+ up to dimension-six condensates, yielding fD+=203.0±1.5MeV. Our result is in good agreement with BESIII measurements and theoretical predictions. We also present the integrated decay widths for the D+-meson in three channels Γ(D+→e+νe)=(5.263−0.075+0.076)×10−21GeV, Γ(D+→μ+νμ)=(2.236−0.032+0.032)×10−16GeV and Γ(D+→τ+ντ)=(5.958−0.085+0.086)×10−16GeV. Accordingly, we compute the branching fractions B(D+→ℓ+νℓ) with the electron, muon and tau channels, which are B(D+→e+νe)=(8.260−0.118+0.119)×10−9, B(D+→μ+νμ)=(3.508−0.050+0.051)×10−4 and B(D+→τ+ντ)=(0.935−0.013+0.013)×10−3. Furthermore, we present our prediction for the CKM matrix element |Vcd| using the branching fraction B(D+→μ+νμ) obtained from BESIII Collaboration, yielding |Vcd|=0.227−0.001+0.002.