Aspects of chiral pion-nucleon physics

The next-to-leading order chiral pion-nucleon Lagrangian contains seven finite low-energy constants. Two can be fixed from the nucleon anomalous magnetic moments and another one from the quark mass contribution to the neutron-proton mass splitting. We find a set of nine observables, which to one-loop order only depend on the remaining four dimension-two couplings. These are then determined from a best fit. We also show that their values can be understood in terms of resonance exchange related to Δ excitation as well as vector and scalar meson exchange. In particular, we discuss the role of the fictitious scalar-isoscalar meson. We also investigate the chiral expansion of the two P-wave scattering volumes P^-₁ and P⁺₂ as well as the isovector S-wave effective range parameter b^- . The one-loop calculation is in good agreement with the data. The difference P^-₁ - P⁺₂ signals chiral loop effects in the πN P-waves. The calculated D-and F-wave threshold parameters compare well with the empirical values.