Low-energy pion-nucleon scattering and the Δ resonance in lattice QCD

We report on our investigation of low-energy pion-nucleon scattering from lattice QCD with Wilson type fermions. Our focus is on the isospin I = 3/2 channel, which couples to the Delta resonance. We discuss our calculations aiming at the extraction of the Delta resonance mass, width and effective coupling at pion mass 250 MeV, using the Lüscher finite-volume method to extract the phase shift δJ=3/2,l=1.

On the spin excitation energy of the nucleon in the Skyrme model

In the Skyrme model of nucleons and nuclei, the spin excitation energy of the nucleon is traditionally calculated by a fit of the rigid rotor quantization of spin/isospin of the fundamental Skyrmion (the hedgehog) to the masses of the nucleon and the Delta resonance. The resulting, quite large spin excitation energy of the nucleon of about [Formula: see text] is, however, rather difficult to reconcile with the small binding energies of physical nuclei, among other problems. Here, we argue that a more reliable interval of values for the spin excitation energy of the nucleon, compatible with many physical constraints is between [Formula: see text] and [Formula: see text]. The fit of the rigid rotor to the Delta, on the other hand, is problematic in any case, because it implies the use of a nonrelativistic method for a highly relativistic system.