Nucleon Polarizibilities for Virtual Photons

Abstract

We generalize the sum rules for the nucleon electric plus magnetic polarizability $\Sigma =\alpha +\beta$ and for the nucleon spin-polarizability $\gamma$, to virtual photons with $Q^2>0$. The dominant low energy cross sections are represented in our calculation by one-pion-loop graphs of relativistic baryon chiral perturbation theory and the $\Delta (1232)$-resonance excitation. For the proton we find good agreement of the calculated ${\Sigma }_p(Q^2)$ with empirical values obtained from integrating up electroproduction data for $Q^2<0.4Ge{V}^2$. The proton spin-polarizability ${\gamma }_p(Q^2)$ switches sign around $Q^2=0.4Ge{V}^2$ and it joins smoothly the "partonic" curve, extracted from polarized deep-inelastic scattering, around $Q^2=0.7Ge{V}^2$. For the neutron our predictions of ${\Sigma }_n(Q^2)$ and ${\gamma }_n(Q^2)$ agree reasonably well at $Q^2=0$ with existing determinations. Upcoming (polarized) electroproduction experiments will be able to test the generalized polarizability sum rules investigated here.

Comments: 12 pages, 5 figures, submittes to Nuclear Physics A