International audienceWe review applications of effective field theory methods in a finite volume for the extraction of the characteristics of unstable particles from lattice QCD calculations. In particular, the scalar mesons f0(980),a0(980) are considered. We formulate criteria that distinguish between hadronic molecules and tightly bound quark states, as well as between the ordinary qq̄ and the tetraquark states. Using these criteria will enable one to study the nature of scalar mesons on the lattice. Further, we also formulate a procedure to calculate resonance matrix elements on the lattice by using the background field method

Using the language of non-relativistic effective Lagrangians, we formulate a systematic framework for the calculation of resonance matrix elements in lattice QCD. The generalization of the Lüscher-Lellouch formula for these matrix elements is derived. We further discuss in detail the procedure of the analytic continuation of the resonance matrix elements into the complex energy plane and investigate the infinite-volume limit.

We calculate the self-energy of the ∆(1232) resonance in a finite volume, using chiral effective field theory with explicit spin-3/2 fields. The calculations are performed up-to-and-including fourth order in the small scale expansion and yield an explicit parameterization of the energy spectrum of the interacting pion-nucleon pair in a finite box in terms of both the quark mass and the box size L. It is shown that finite-volume corrections can be sizeable at small quark masses.

Using non-relativistic effective field theory in 1+1 dimensions, we generalize Lüscher's approach for resonances in the presence of an external field. This generalized approach provides a framework to study the infinite-volume limit of the form factor of a resonance determined in lattice simulations.