The mass of the Δ resonance in a finite volume: fourth-order calculation

We calculate the self-energy of the Δ(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 para\-meterization 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.