Generalized dipole polarizabilities and the spatial structure of hadrons

We present a phenomenological discussion of spin-independent, generalized dipole polarizabilities of hadrons entering the virtual Compton scattering process g*h!gh. We introduce a new method of obtaining a tensor basis with appropriate Lorentz-invariant amplitudes which are free from kinematical singularities and constraints. The result is summarized in terms of a compact effective Lagrangian. We then motivate a gaugeinvariant separation into a generalized Born term containing ground-state properties only and a residual contribution describing the model-dependent internal structure. The generalized dipole polarizabilities are defined in terms of Lorentz-invariant residual amplitudes. Particular emphasis is laid on a physical interpretation of these quantities as characterizing the spatial distributions of the induced electric polarization and magnetization of hadrons. It is argued that three dipole polarizabilities—namely, the longitudinal electric a L(q 2 ), the transverse electric a T(q 2 ), and the magnetic b(q 2 ) ones—are required in order to fully reconstruct local polarizations induced by soft external fields in a hadron. One of these polarizabilities, a T(q 2 ), describes an effect of higher order in the soft final-photon momentumq8. We argue that the associated spatial distributions obtained via Fourier transforms in the Breit frame are meaningful even for such a light particle as the pion. The spatial distributions are determined at large distances r;1/mp for pions, kaons, and octet baryons by the use of chiral perturbation theory.