The BESIII collaboration has reported the precision measurement of the branching fraction of the leptonic decay D⁺→μ⁺ν_μ. This result has been published in Physical Review Letters on 04 August 2025. [Phys. Rev. Lett. 135, 061801 (2025)].
Leptonic D⁺ decays provide a unique insight for understanding the decay mechanisms of charm quark. In the Standard Model, the leptonic D⁺ decays involve the strong and weak interactions, which can be parameterized by the decay constant f_D+ and the quark mixing-matrix (CKM matrix) element |V_cd| (which is one of fundamental constants of the Standard Model), respectively. Based on the precisely measured branching fraction of D⁺→μ⁺ν_μ, one can determine the product of f_D+ and |V_cd|. The obtained f_D+ and |V_cd| are critical to test the lattice quantum chromodynamics (LQCD) calculations and the CKM matrix unitarity, respectively. This is one of fundamental measurements in hadron physics field! This measurement made it possible to extract |V_ub| and |V_cb|, which played an indispensable role in testing the unitary nature of the CKM matrix.

Previously, LQCD calculation on f_D+ reached a precision of 0.2% and BESIII reported a measurement of D⁺→μ⁺ν_μ by analyzing data taken in 2010-2011. Based on full 20.3 fb^-1 of e⁺e^- annihilation data collected at the center-of-mass energy of 3.773 GeV in 2010-2011 and 2022-2024, BESIII measures the branching fraction of D⁺→μ⁺ν_μ with unprecedent precision to be B(D⁺→μ⁺ν_μ)=(4.034±0.080_stat±0.040_syst)×10^-4. The product of f_D+ and |V_cd| is determined to be (48.02±0.48_stat±0.24_syst±0.12_input ±0.15_EM) MeV. This result is a factor of 2.3 more precise than the previous best measurement. Using the value of the |V_cd| given by the global standard model fit, we obtain f_D+= (213.5±2.1_stat±1.1_syst±0.8_input ±0.7_EM) MeV. Alternatively, using the value of f_D+ from a precise LQCD calculation, we extract |V_cd|= 0.2265 ± 0.0023_stat ± 0.0011_syst ±  0.0009_input ± 0.0007_EM.

Figure 1 exhibits the signal of D⁺→μ⁺ν_μ as well as the comparison of the f_D+ measured in this work, other measurements and those given by different LQCD predictions.

Reference: Phys. Rev. Lett. 135, 061801 (2025)
Journal link: https://link.aps.org/doi/10.1103/0b8v-4rnh

Fig. 1: (left) The signal of D⁺→μ⁺ν_μ and (right) the comparison of the f_D+ measured in this work, other measurements and those given by different LQCD predictions.