Generalized dipole polarizabilities and the spatial structure of hadrons -art. no. 015203

We present a phenomenological discussion of spin-independent, generalized d ipole polarizabilities of hadrons entering the virtual Compton scattering p rocess gamma *h-->gammah. We introduce a new method of obtaining a tensor b asis with appropriate Lorentz-invariant amplitudes which are free from kine matical singularities and constraints. The result is summarized in terms of a compact effective Lagrangian. We then motivate a gauge-invariant separat ion into a generalized Born term containing ground-state properties only an d a residual contribution describing the model-dependent internal structure . The generalized dipole polarizabilities are defined in terms of Lorentz-i nvariant residual amplitudes. Particular emphasis is laid on a physical int erpretation of these quantities as characterizing the spatial distributions of the induced electric polarization and magnetization of hadrons. It is a rgued that three dipole polarizabilities-namely, the longitudinal electric alpha (l)(q(2)), the transverse electric alpha (T)(q(2)), and the magnetic beta (q(2)) ones-are required in order to fully reconstruct local polarizat ions induced by soft external fields in a hadron. One of these polarizabili ties, alpha (T) (q(2)), describes an effect of higher order in the soft fin al-photon momentum q'. We argue that the associated spatial distributions o btained via Fourier transforms in the Breit frame are meaningful even for s uch a light particle as the pion. The spatial distributions are determined at large distances r similar to1/m(pi) for pious, kaons, and octet baryons by the use of chiral perturbation theory.