Inclusive semileptonic decays of the $D_{s}$ meson: Lattice QCD confronts experiments

Abstract: We present the results of a first-principles theoretical study of the inclusive semileptonic decays of the $D_{s}$ meson. We performed a state-of-the-art lattice QCD calculation by taking into account all sources of systematic errors. A detailed discussion of our lattice calculation, demonstrating that inclusive semileptonic decays can nowadays be studied on the lattice at a phenomenologically relevant level of accuracy, is the subject of a companion paper [1]. Here we focus on the phenomenological implications of our results. Using the current best estimates of the relevant Cabibbo-Kobayashi-Maskawa (CKM) matrix elements, our theoretical predictions for the decay rate and for the first two lepton-energy moments are in very good agreement with the corresponding experimental measurements. We also argue that, while the inclusive $D_{s}$ channel is not yet competitive with the exclusive channels in the $|V_{cs}|$ determination, the situation can be significantly improved in the near future.