Heavy-particle-induced effective lagrangian in spontaneously broken theories: (I). The σ-model

Abstract

The general formalism which has been recently developed to study virtual heavy-particle effects is extended to the case of spontaneously broken theories. In the present paper, we give a detailed analysis for the spontaneously broken linear σ-model, with an explicit soft-symmetry-breaking term included to render Goldstone pions small mass. We derive a low-energy effective local lagrangian for pions, with which arbitrary low-energy pion Green functions may be calculated systematically to any desired accuracy in inverse powers of the mass parameter of the fluctuation fields, s = σ − 〈 σ〉. We also discuss the connection of our results to the non-linear σ-model. Our approach provides a new field-theoretical basis for the chiral perturbation theory and soft pion physics.