Generalized dipole polarizabilities of the pion

Abstract

We discuss the virtual Compton scattering amplitude $γ^\ast+π\to γ+π$ which enters the reaction $π^-+e^-\toπ^-+e^-+γ$. The low-energy scattering amplitude is divided into a model-independent part, involving only the electromagnetic form factor, and a residual part which contains structure information related specifically to (virtual) Compton scattering. In the limit of vanishing final-photon energy, the residual amplitude can be expressed in terms of three generalized dipole polarizabilities which are functions of the squared virtual-photon four-momentum. We study the VCS amplitude in the framework of chiral perturbation theory at ${\cal O}(p^4)$. At the one-loop level the generalized dipole polarizabilities are degenerate $α_L(q^2)=α_T(q^2)=-β(q^2)$.