The BESIII collaboration has reported “Precise Measurement of the Form Factors in D⁰→K^*(892)^-μ⁺ν_μ  and Test of Lepton Universality with D⁰→K^*(892)^-l⁺ν_l  Decays”. These results have been published in Physical Review Letters on 10 September 2025. [Phys. Rev. Lett. 135, 111803 (2025)].

Semileptonic (SL) decays of charmed mesons provide valuable information on the weak and strong interactions with hadrons composed of heavy quarks. The partial rate of the decay is related to the product of the hadronic form factor (FF) describing the effects of the strong interaction in the initial and final hadrons, and the Cabibbo-Kobayashi-Maskawa (CKM) matrix element |V_cd| parametrizing the mixing of quarks in the weak interaction. Due to |Vcd| being tightly constrained by CKM unitarity, studies of D meson SL decays provide an ideal laboratory to extract the hadronic FFs. In theory, calculations on the FFs in the D→K^*(892) transition are extensively carried out by a series of non-perturbative approaches. However, the calculated FFs from these theories differ significantly. Therefore, precise measurements of the FFs can provide stringent tests and rigorous calibrations on various non-perturbative calculations. Furthermore, these data also represent a valuable motivation for updating the LQCD calculation.

In this work, using 7.9/fb of e⁺e^- annihilation data collected at 3.773 GeV with the BESIII detector, we report the first measurement of the branching fraction (BF) for D⁰→K^*(892)^-μ⁺ν_μ and measure its BF to be (1.373±0.020±0.023)%. Under the assumption of the isospin symmetry, we provide the most precise determination of the BF for D⁰→K^*(892)^-μ⁺ν_μ and measure BF[D⁰→K^*(892)^-μ⁺ν_μ]=(1.948±0.033±0.036)%. Combining the BF of D⁰→K^*(892)^-e⁺ν_e that we previously reported in JHEP 03(2025) 197, we obtain the relative ratio of the BFs between μ and e modes to be Rμ/e = 0.955±0.020±0.017, which provides a high-quality and precise validation of the lepton flavour universality (LFU) predicted by the standard model with the D⁰→K^*(892) transition.  

In addition, based on partial wave analysis of the dynamics in the D⁰→K^*(892)^-μ⁺ν_μ decay, we measure the FF parameters at the q²=0 to be r_V=V(0)/A₁(0)=1.46±0.11±0.04 and r₂=A₂(0)/A₁(0)=0.71±0.08±0.03, where V(0) is the vector FF and A_1,2(0) is the axial FF. Combining the results that we previously reported in D⁰→K_s⁰π^-e⁺ν_e and D⁰→K^-π⁰μ⁺ν_μ decays, we obtain the most precise measurements of the FF parameters in D⁰→K^*(892) transition. We measure r_V=1.456±0.040±0.016 and r₂=0.715±0.031±0.014, and  A₁(0)=0.614±0.005±0.004. The measured FFs (r_V and r₂ ) disfavour the central values calculated from the HMχT, CLFQM, RQM by more than 3 standard deviations.

Reference: Phys. Rev. Lett. 135, 111803 (2025)
Journal link: https://doi.org/10.1103/zfxr-dlzg  
        

Figure 1：Comparisons of the measured BF[D⁰→K^*(892)^-μ⁺ν_μ] and A₁(0) in this work with various theoretical calculations。
                                

Figure 2：Comparisons of  measured r_V and r₂ in this work with various theoretical calculations.