Towards the P-wave nucleon-pion scattering amplitude in the ∆(1232) channel

Abstract

We use lattice QCD and the Lüscher method to study elastic pion-nucleon scattering in the isospin I = 3/2 channel, which couples to the ∆(1232) resonance. Our Nf = 2 + 1 flavor lattice setup features a pion mass of mπ ≈ 250 MeV, such that the strong decay channel ∆ → πN is close to the threshold. We present our method for constructing the required lattice correlation functions from single- and two-hadron interpolating fields and their projection to irreducible representations of the relevant symmetry group of the lattice. We show preliminary results for the energy spectra in selected moving frames and irreducible representations, and extract the scattering phase shifts. Using a Breit-Wigner fit, we also determine the resonance mass m∆ and the g∆−πN coupling.