Nucleon polarizabilities for virtual photons

We generalize the sum rules for the nucleon electric plus magnetic polarizability Σ = α + β and for the nucleon spin-polarizability γ, to virtual photons with Q² > 0. The dominant low energy amplitudes are represented in our calculation by one-pion-loop graphs of relativistic baryon chiral perturbation theory and the Δ(1232)-resonance excitation. For the proton we find good agreement of the calculated Σ_p(Q²) with empirical values obtained from integrating up electroproduction data for Q² < 0.4 GeV². The proton spin-polarizability γ_p(Q²) switches sign around Q² = 0.4 GeV² and it joins smoothly the "partonic" curve, extracted from polarized deep-inelastic scattering, around Q² = 0.7 GeV². For the neutron our predictions of Σ_n(Q²) and γ_n(Q²) agree reasonably well at Q² = 0 with existing determinations. Upcoming (polarized) electroproduction experiments will be able to test the generalized polarizability sum rules investigated here.