English

We present the determination of the ∆ (1232) resonance parameters using lattice QCD and the Lüscher method. The resonance couples to the elastic pion-nucleon scattering with Jᴾ = 3/2⁺ in the isospin I = 3/2 P-wave channel. Our Nf = 2 + 1 flavor lattice setup features a pion mass of mπ ≈ 250 MeV, such that the strong decay channel ∆ → π N is open for decay. We use the projection method for constructing the required lattice correlation functions from single- and two-hadron interpolating fields and their projection to irreducible representations of the lattice’s relevant symmetry group. We show the energy spectra results in selected moving frames and irreducible representations and extract the scattering phase shifts P33 and S31. From the determined pole position of the ∆ (1232), we derive the resonance mass m∆ = 1378(7) (9) MeV and the coupling g∆−π N = 23.8 (2.78) (0.9).