Physical Review D
We determine the Δ(1232) resonance parameters using lattice QCD and the Lüscher method. The resonance occurs in elastic pion-nucleon scattering with JP = 3/2+ in the isospin I=3/2, P-wave channel. Our calculation is performed with Nf = 2+1 flavors of clover fermions on a lattice with L ≈ 2.8 fm. The pion and nucleon masses are mπ = 255.4 (1.6) MeV and mN = 1073(5) MeV, respectively, and the strong decay channel Δ → πN is 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 = 2πL(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 mΔ = 1378(7)(9) MeV and the coupling gΔ-πN = 23.8(2.7)(0.9).
Original Publication Citation
Silvi, G., Paul, S., Alexandrou, C., Krieg, S., Leskovec, L., Meinel, S., . . . Todaro, A. (2021). P-wave nucleon-pion scattering amplitude in the Δ(1232) channel from lattice QCD. Physical Review D, 103(9), Article 094508, 1-17. https://doi.org/10.1103/PhysRevD.103.094508.
Silvi, Giorgio; Paul, Srijit; Alexandrou, Constantia; Krieg, Stefan; Leskovec, Luka; Meinel, Stefan; Negele, John; Petschlies, Marcus; Pochinsky, Andrew; Rendon, Gumaro; Syritsyn, Sergey; and Todaro, Antonio, "P-Wave Nucleon-Pion Scattering Amplitude in the Δ(1232) Channel from Lattice QCD" (2021). Physics Faculty Publications. 528.