Speaker
Description
Spectral densities encode key QCD observables, including hadronic decay rates, cross sections, and transport properties of the quark-gluon plasma. Their Laplace transform corresponds to Euclidean correlation functions, which can be accessed non-perturbatively from first-principles lattice QCD. In this talk, we present analytic formulae to carry out the inverse Laplace transform so as to extract spectral densities from either the continuum or the discrete sampling of correlation functions in the Euclidean time. We first define the spectral observable, possibly regulated and/or smeared, in terms of continuum integral transforms. We then discuss proper modifications for the case where correlation functions are available on a discrete lattice, and explicitly show that the proposed lattice solution tends to its continuum counterpart up to $O(a^2)$ effects if the lattice correlator is $O(a)$-improved.