We use lattice QCD and the Luscher method to study elastic pion-nucleon scattering in the isospin $I = 3/2$ channel, which couples to the $Delta(1232)$ resonance. Our $N_f=2+1$ flavor lattice setup features a pion mass of $m_pi approx 250$ MeV, such that the strong decay channel $Delta rightarrow pi N$ 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 $m_Delta$ and the $g_{Delta-pi N}$ coupling.
Download