Chiral symmetry breaking and the σ-term in pion-nucleon scattering

One of the most important test grounds of current algebra and PCAC and recently of chiral perturbation theory of QCD is low energy pion‐nucleon scattering. A crucial number is the pion‐nucleon σ‐term, which is a measure of explicit chiral‐symmetry breaking of QCD due to the quark mass term in the QCD Lagrangian.There exists presently an unresolved discrepancy between the πN on‐shell amplitude Σ at the unphysical Cheng‐Dashen point t=2 m2π, ν=(s‐u)/4 mN=0 obtained via forward dispersion relations from the Karlsruhe‐Helsinki pion‐nucleon phase shifts and the σ‐term evaluated from the baryon spectrum by chiral perturbation theory of QCD. Chiral perturbation theory relates the two quantities Σ and σ by Σ=σ+4...5 MeV. The dispersion analysis results in Σ=(65±8) MeV and the chiral perturbation calculation in σ=(35±5) Mev. The discrepancy hints either at theoretical deficiencies or at an insufficient πN data basis. Experimental low energy πp data (Tπ≲100 Mev) are of particular significance to solve this problem, but unfortunately partly contradictory. Recent πN experiments as well as future experiments, the aims of which are to resolve present contradictions, will be discussed.