The Cabibbo–Kobayashi–Maskawa (CKM) matrix encodes the strengths of flavour-changing quark transitions mediated by the W boson. Its entries are fundamental parameters of the Standard Model, and their precise determination is a central goal of flavour physics. Within the Standard Model, decay rates of B and charm mesons can be predicted in terms of CKM matrix elements, including for leptonic decays such as B → ℓν and semileptonic channels like B → D(*)ℓν and B → πℓν. Experiments including Belle II at KEK then measure these rates to determine the corresponding CKM elements.
As pure-QCD predictions have reached sub-percent precision, electromagnetic corrections must now also be included. For heavy mesons, their internal structure plays an important role in radiative leptonic decays. In this talk, I will present our lattice-QCD approach to predicting decay rates for processes such as B → ℓνγ in terms of QCD form factors, and discuss ongoing analyses based on a set of JLQCD gauge ensembles. This type of lattice calculations begun only recently, and so I will explain why these decays can be studied in Euclidean space. I will also describe our strategy for controlling the leading systematic uncertainty from excited-state contamination. This approach also allows us to access a broad range of photon energies and several initial mesons, including D, Ds, B, and Bc. This work will provide a more complete understanding of the hadronic structure of these mesons and help construct infrared-safe observables, such as the radiation-inclusive decay B → ℓν[γ]. Ultimately, it will reduce theoretical systematic uncertainties in the extraction of CKM matrix elements.