Aspects of the ETH model of the pion-nucleon interaction

The ETH model of the pion-nucleon (πN) interaction contains t-channel σ- and ρ-exchange graphs, as well as the s- and u-channel contributions with the well-established s and p baryon states with masses below 2 GeV as virtual particles; the model amplitudes obey crossing symmetry and isospin invariance. In the present work, we give the analytical expressions for the model contributions to the K-matrix elements up to (and including) the f waves. We also extract a new phase-shift solution after performing a partial-wave analysis of meson-factory π±p elastic-scattering data below 100 MeV; included in our results now are also the effects of the variation of the σ-meson mass in the interval which is currently recommended by the Particle-Data Group. Finally, we revisit the subject of the πN Σ term and, using the model amplitudes, obtain Σ=72.4±3.1 MeV. Our prediction agrees well with the result extracted with Olsson's method, after a few flaws in his paper [61] were corrected.