Speaker: Agostino Patella

Title: Spectral densities from the lattice: explorations in the O(3) non-linear sigma model

Abstract:
QCD spectral densities are interesting intermediate quantities related to a number of physical observables. For instance, the R-ratio, i.e. the properly normalized total cross section of the process (e+ e- -> hadrons), can be expressed in terms of the spectral density of the electromagnetic current. The non-perturbative nature of QCD prevents us to use analytic methods to calculate observables at low energy, and one would like to understand whether it is possible to use lattice simulations to calculate spectral densities at low energies. In this talk, I will explain how spectral densities are defined, why they are phenomenologically interesting and why it is difficult to calculate them in the context of lattice simulations. I will discuss a particular method that has been put forward recently, based on the idea that one can approximate smeared spectral densities and I will show how this method works in a toy model, i.e. in the O(3) non-linear sigma model.