The Δ-resonance in a finite volume

We study the extraction of Δ-resonance parameters from lattice data for small quark masses, corresponding to the case of an unstable Δ. To this end, we calculate the spectrum of the correlator of two Δ-fields in a finite Euclidean box up-to-and-including O(ϵ3)O(ϵ3) in the small scale expansion using infrared regularization. On the basis of our numerical study, we argue that the extraction of the parameters of the Δ-resonance (in particular, of the mass and the pion–nucleon–delta coupling constant) from the measured volume dependence of the lowest energy levels should be feasible.