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On the prediction of spectral densities from Lattice QCD
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Hadronic spectral densities play a pivotal role in particle physics, a prime example being the R-ratio defined from electron-positron scattering into hadrons. To predict them from first principles using Lattice QCD, we face a numerically ill-posed inverse problem, due to the Euclidean signature adopted in practical simulations. Here we present a recent numerical analysis of the vector isovector spectral density extracted using the multi-level algorithm (recently extended also to the case of dynamical fermions) and discuss its implications.
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Spectral densities from Euclidean-time lattice correlation functions
A Tikhonov-regularized inverse Laplace transform built on the Mellin basis extracts spectral densities from Euclidean correlators, with an exact discrete-lattice version and controlled smearing kernels.
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