Generalized dipole polarizabilities and the spatial structure of hadrons
A. I. L’vov, S. Scherer, B. Pasquini, C. Unkmeir, and D. Drechsel
Phys. Rev. C 64, 015203 (2001) - Published 18 June, 2001
We present a phenomenological discussion of spin-independent, generalized dipole polarizabilities of hadrons entering the virtual Compton scattering process 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 gauge-invariant 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 the transverse electric and the magnetic ones—are required in order to fully reconstruct local polarizations induced by soft external fields in a hadron. One of these polarizabilities, describes an effect of higher order in the soft final-photon momentum 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 for pions, kaons, and octet baryons by the use of chiral perturbation theory.