BARYON CHIRAL DYNAMICS

Abstract

Many of the constraints of chiral symmetry on the interaction of pions and nucleons at low energies were worked out long before the advent of QCD (Current algebra, PCAC). Later it was realized that the corrections to these symmetry relations can be obtained by implementing the chiral symmetry and its breaking by the quark masses into an effective Lagrangian describing the interaction of mesons and baryons. This method is called chiral perturbation theory (CHPT).l It allows one to compute the expansion of QCD amplitudes and transition currents in powers of the external momenta and quark masses; it has become one of the standard tools to analyze the strong interactions at low energy. Over the last few years, the progress in this field in the baryon sector has been twofold: on one hand, we have reached a new level of precision in many of the classical applications: by now, the full one loop result for the nucleon form factors and the pion-nucleon scattering amplitude in the isospin limit is k n ~ w n . ~ ~ ~ Even the first two-loop result has been obtained: the chirai expansion of the nucleon mass has been worked out to fifth order.4 On the other hand, the framework has been extended and applied to a whole range of new processes: the effective Lagrangian has been extended to include electromagnetism, making it possible to disentangle strong and electromagnetic isospin ~ io l a t ion .~ This effective theory of QCD+QED has been used to calculate next-to-leading order isospin violating effects in the pion-nucleon scattering amplitude6 and to study the properties of the r p bound state.7 Another extension of the framework incorporates the A-resonance as an explicit degree of freedom into the effective Lagrangian, thereby summing up the potentially large higher-order terms in the chiral expansion associated with this resonance.a Despite all of this impressive progress, we are still short of having the answers to some very old questions, like, for example, what is the value of the