Hadronic spectral densities from Euclidean lattice QCD correlators

This Thesis tackles the challenging problem of extracting hadronic spectral densities from Eu clidean correlation functions computed via lattice QCD simulations. Using the HLT method that allows to compute smeared spectral functions with controlled statistical and systematic uncertainties, we achieved the first-ever first-principles calculation of the R-ratio and a non OPE-based determination of the CKM matrix element |Vus| from the τ lepton’s hadronic decay. Tensions between theory and experiments emerge in both our works which require further in vestigation from both the sides. On the methodological perspective, we developed an innovative method based on Machine Learning whose main features are a model independent training strategy that we implemented by parametrizing the training data over a functional space and a reliable estimate of the systematic uncertainties that we achieved by introducing an ensemble of machines. The method, validated in full generality, showed a remarkable agreement with HLT. Current projects and future directions are also outlined.