Chiral symmetry breaking and meson-nucleon sigma commutators: A review

Chiral symmetries are discussed in considerable detail, and their importance and consequences for the study of elementary particle physics are reviewed. For the study of broken symmetries we concentrate mainly on meson-nucleon sigma terms, $\pi \pi$ scattering, and $K_{l3\mathrm{}}$ decays. In addition to giving a critical and detailed review of most of the "experimental" estimates for pion-nucleon and kaon-nucleon sigma terms done so far, we also outline the most common chiral symmetry-breaking schemes at present, such as $(3,\overline{3})+(\overline{3},3)$, $(6,\overline{6})+(\overline{6},6)$, (8,8) and (1, 8) + (8, 1) representations of SU(3) × SU(3) and possible mixtures of them, and discuss and compare their predictions with experiment. Nonlinear effective Lagrangians are briefly discussed, and the connection between broken scale invariance and chiral symmetry breaking is outlined, with emphasis on our present knowledge of meson-nucleon sigma terms.