Recent Developments in Chiral Perturbation Theory

Abstract

I review recent developments in chiral perturbation theory (CHPT) which is the effective field theory of the standard model below the chiral symmetry breaking scale. The effective chiral Lagrangian formulated in terms of the pseudoscalar Goldstone bosons ($π, \, K, \, η$) is briefly discussed. It is shown how one can gain insight into the ratios of the light quark masses and to what extent these statements are model--independent. A few selected topics concerning the dynamics and interactions of the Goldstone bosons are considered. These are $ππ$ and $πK$ scattering, some non--leptonic kaon decays and the problem of strong pionic final state interactions. CHPT also allows to make precise statements about the temperature dependence of QCD Green functions and the finite size effects related to the propagation of the (almost) massless pseudoscalar mesons. A central topic is the inclusion of matter fields, baryon CHPT. The relativistic and the heavy fermion formulation of coupling the baryons to the Goldstone fields are discussed. As applications, photo--nucleon processes, the $πN$ $Σ$--term and non--leptonic hyperon decays are presented. Implications of the spontaneously broken chiral symmetry on the nuclear forces and meson exchange currents are also described. Finally, the use of effective field theory methods in the strongly coupled Higgs sector and in the calculation of oblique electroweak corrections is touched upon.