P-wave nucleon-pion scattering amplitude in the Δ(1232) channel from lattice QCD

We determine the Δ(1232) resonance parameters using lattice QCD and the Lüscher method. The resonance occurs in elastic pion-nucleon scattering with J^P= 3/2⁺in the isospin I = 3/2, P-wave channel. Our calculation is performed with N_f= 2 + 1 flavors of clover fermions on a lattice with L ≈ 2.8 fm. The pion and nucleon masses are m_π= 255.4 (1.6) MeV and m_N= 1073 (5) MeV, espectively, and the strong decay channel Δ π_Nis found to be above the threshold. To thoroughly map out the energy dependence of the nucleon-pion scattering amplitude, we compute the spectra in all relevant irreducible representations of the lattice symmetry groups for total momenta up to P^→= 2π/L (1, 1, 1), including irreps that mix S and P waves. We perform global fits of the amplitude parameters to up to 21 energy levels, using a Breit-Wigner model for the P-wave phase shift and the effective-range expansion for the S-wave phase shift. From the location of the pole in the P-wave scattering amplitude, we obtain the resonance mass m_Δ= 1378(7)(9) MeV and the coupling g_Δ-πN= 23.8(2.7)(0.9).