Real photon emissions in leptonic decays

We present a non-perturbative calculation of the form factors which contribute to the amplitudes for the radiative decays P → `ν¯`γ, where P is a pseudoscalar meson and ` is a charged lepton. Together with the non-perturbative determination of the virtual photon corrections to the processes P → `ν¯` , this will allow accurate predictions to be made at O(αem) for leptonic decay rates for pseudoscalar mesons ranging from the pion to the B meson. We are able to separate unambiguously the point-like contribution, the square of which leads to the infrared divergence in the decay rate, from the structure dependent, infrared-safe, terms in the amplitude. The fully non-perturbative, O(a) improved calculation of the inclusive leptonic decay rates will lead to significantly improved precision in the determination of the corresponding Cabibbo-KobayashiMaskawa (CKM) matrix elements. Precise predictions for the emission of a hard photon are also very interesting, especially for the decays of heavy D and B mesons for which currently only model-dependent predictions are available to compare with existing experimental data.