Inclusive semileptonic decays of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>D</mml:mi><mml:mi>s</mml:mi></mml:msub></mml:math> meson: A first-principles lattice QCD calculation

We present the results of a first-principles theoretical study of the inclusive semileptonic decays of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>D</a:mi><a:mi>s</a:mi></a:msub></a:math> meson. We performed a state-of-the-art lattice QCD calculation using the gauge ensembles produced by the Extended Twisted Mass Collaboration with dynamical light, strange and charm quarks with physical masses and employed the so-called Hansen-Lupo-Tantalo (HLT) method to extract the decay rate and the first two lepton-energy moments from the relevant Euclidean correlators. We have carefully taken into account all sources of systematic errors, including the ones associated with the continuum and infinite-volume extrapolations and with the HLT spectral reconstruction method. We obtained results in very good agreement with the currently available experimental determinations and with a total accuracy at the few-percent level, of the same order of magnitude of the experimental error. Our total error is dominated by the lattice QCD simulations statistical uncertainties and is certainly improvable. From the results presented and thoroughly discussed in this paper we conclude that it is nowadays possible to study heavy mesons inclusive semileptonic decays on the lattice at a phenomenologically relevant level of accuracy. The phenomenological implications of our physical results are the subject of a companion Letter [A. De Santis , Inclusive semileptonic decays of the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>D</c:mi><c:mi>s</c:mi></c:msub></c:math> meson: Lattice QCD confronts experiments, , 121901 (2025).].