A theoretical approach to low energy pion physics

Abstract

We wish to propose a new approach for the study of problems involving low energy pions.The method starts from a determination of the pion-nucleon scattering state vector in terms of the physical nucleon state vector and of the renormalized coupling constant.Such a determination can be performed in the one-meson approximation and leads in a simple and natural way to the same results as the Chew and Low approach to scattering and photoproduction.The method is then applied to the problem of radiative pion-nucleon scattering where we obtain an expression for the T matrix in a closed form which has the same degree of validity as the result for photoproduction.Although the method has its natural field of application in the framework of the static model, it can be applied to obtain the recoil effects due to the motion of the physical nucleon. In the case of pion-nucleon scattering we obtain results closely analogous to those obtained in the framework of relativistic dispersion theory.