  Spectral densities encode non-perturbative information that enters the
calculation of a plethora of physical observables in strongly coupled field
theories. Phenomenological applications encompass aspects of standard-model
hadronic physics, observable at current colliders, as well as correlation
functions characterizing new physics proposals, testable in future experiments.
By making use of numerical data produced with lattice gauge theories, we
perform a systematic study to demonstrate the effectiveness of recent
technological progress in the reconstruction of spectral densities. To this
purpose, we write and test new software packages that use energy-smeared
spectral densities to analyze the mass spectrum of mesons. We assess the
effectiveness of different smearing kernels and optimize the smearing
parameters to the characteristics of available lattice ensembles. For
concreteness, we analyze the Sp(4) lattice gauge theory with matter
transforming in an admixture of fundamental and 2-index antisymmetric
representations of the gauge group. We generate new ensembles for this theory,
with lattices that have a longer extent in the time direction with respect to
the spatial ones. We run our tests on these ensembles, obtaining new results
about the spectrum of light mesons and their excitations. We make available our
algorithm and software for the extraction of spectral densities, that can be
applied to theories with other gauge groups, including the theory of strong
interactions (QCD) governing hadronic physics in the standard model.
