The BESIII collaboration recently reported a test of Lepton Universality and precise measurement of the Form Factors of D⁰→K^* (892)^- μ⁺ ν_μ based on 7.93 fb-1 data collected at the center-of-mass energy of 3.773 GeV. The results have been published recently in Physics Review Letters on January 2, 2025 [Phys. Rev. Lett. 134, 011803 (2025)].

Semileptonic D decays provide a good opportunity to both rigorously test the Standard Model through lepton flavor universality and to explore the weak and strong interactions in mesons composed of heavy quarks. The SL partial decay width is related to the product of the hadronic form factors (FFs) describing the strong interactions in the initial and final hadrons, including non-perturbative effects of Quantum Chromodynamics (QCD), and a Cabibbo-Kobayashi-Maskawa (CKM) matrix element. Thus, precise measurements of FFs are important for testing the theoretical predictions where decay rates are calculated from first principles.
In this work, we report the first measurement of the absolute BF for the D⁰→K^- π⁰ μ⁺ ν_μ decay and investigate its dynamics. We perform the first amplitude analysis for the D⁰→K^- π⁰ μ⁺ ν_μ decay and observe an S wave component with a fraction f_{S wave}=(5.76±0.35± 0.29)%, resulting in B[D⁰→K^- π⁰_{S wave} μ⁺ ν_μ]=(4.223 ± 0.268±0.222)×10^-4. The dominant P wave component is observed with a fraction of f_{K* (892)-} =(94.24±0.35±0.29)%, leading to B(D⁰→K^* (892)^- μ⁺ ν_μ)=(2.073±0.039±0.032)%. This result is consistent with previous measurement and has improved in precision by a factor of 5 over the current world average.  Benefiting from the improved precision, our result disfavors the covariant quark model (CQM) and the covariant confining quark model (CCQM) calculations for the first time, while it supports the so-called chiral unitary approach and light-cone sum rules (LCSR) calculations. Combining with the previously most precise measurement of B(D⁰→K^* (892)^- μ⁺ ν_μ), we provide a stringent test of the μ-e lepton flavor universality with D⁰→K^* (892)^- l⁺ ν_l. No evidence of LFU violation is found with current statistics. Furthermore, the most precise FF ratios of the D⁰→K^* (892)^- μ⁺ ν_μ decay are determined to be r_V=1.37±0.09±0.03 and r₂=0.76±0.06±0.02.The results are consistent with the CQM, the CCQM, the light-front quark model, and the LCSR calculations, and they disfavor the HM_χ T model (based on the combination of heavy meson and chiral symmetries) calculation. Our high-precision measurements have effectively advanced the study of the dynamics of semileptonic decays of charmed mesons in the non-perturbative region, providing stricter constraints for the development of QCD theory.

 FIG. 1. Fits to Umiss distributions of the candidate events and projections onto five kinematic variables for D⁰→K^- π⁰ μ⁺ ν_μ. The dots with error bars are data, the blue lines are the fit results, and the dashed lines show the background contributions.

Further reading:
UL: https://link.aps.org/doi/10.1103/PhysRevLett.134.011803
DOI：10.1103/PhysRevLett.134.011803