A proposal by Lüscher enables one to compute the scattering phases of elastic two-body systems from the energy levels of the lattice Hamiltonian in a finite volume. In this work we generalize the formalism to S-, P -and D-wave meson and baryon resonances, and general total momenta.Employing nonvanishing momenta has several advantages, among them making a wider range of energy levels accessible on a single lattice volume and shifting the level crossing to smaller values of m π L.

A new method based on the concept of probability distribution is proposed to analyze the finite volume energy spectrum in lattice QCD. Using synthetic lattice data, we demonstrate that for the channel with quantum numbers of the ∆-resonance a clear resonance structure emerges in such an analysis. Consequently, measuring the volumedependence of the energy levels in lattice QCD will allow to determine the mass and the width of the ∆ with reasonable accuracy.

Using effective field theory methods, we discuss the extraction of the mass and width of the scalar mesons f 0 (980) and a 0 (980) from the finite-volume spectrum in lattice QCD. In particular, it is argued that the nature of these states can be studied by invoking twisted boundary conditions, as well as investigating the quark mass dependence of the spectrum.