Compton scattering from a pion and off-shell effects

Abstract

We discuss the most general form of the electromagnetic vertex of an off-shell pion. The framework of chiral perturbation theory is used to illustrate the representation dependence of the electromagnetic three-point Green's function. For that purpose we discuss the concept of field transformations which, in comparison with the standard Gasser and Leutwyler Lagrangian, generate equivalent Lagrangians containing additional terms at order p^4 proportional to the lowest-order equation of motion. We consider Compton scattering from a pion to show that calculations involving different off-shell effects in the s- and u-channel pole diagrams may nevertheless lead to the same on-shell Compton scattering amplitude. This is a result of the equivalence theorem which states that two equivalent Lagrangians predict the same S-matrix elements even though they may generate a different off-shell behaviour of Green's functions. We conclude that off-shell effects are not only model dependent but also representation dependent