Dispersion effects in nucleon polarizabilities

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Abstract
We present a formalism to extract the dynamical nucleon polarizabilities defined via a multipole expansion of the structure amplitudes in nucleon Compton scattering. In contradistinction to the static polarizabilities, dynamical polarizabilities gauge the response of the internal degrees of freedom of a composed object to an external, real photon field of arbitrary energy. Being energy dependent, they therefore contain additional information about dispersive effects induced by internal relaxation mechanisms, baryonic resonances, and meson production thresholds of the nucleon. We give explicit formulae to extract the dynamical electric and magnetic dipole as well as quadrupole polarizabilities from low-energy nucleon Compton scattering up to the one-pion production threshold, and discuss the connection to the definition of static nucleon polarizabilities. As a concrete example, we examine the results of leading order heavy baryon chiral perturbation theory for the four leading spin-independent isoscalar polarizabilities of the nucleon. Finally, we consider the possible role of energy-dependent effects in low-energy extractions of the isoscalar dipole polarizabilities from Compton scattering on the deuteron.