Generalized Electric Polarizability of the Proton from Skyrme Model

We calculate the electric polarizability $\alpha (q^2)$ of the proton in virtual Compton scattering using the Skyrme model. The $q^2$ dependence of the polarizability is comparable with the predictions obtained from the non-relativistic quark model and the linear sigma model. The chiral behaviors of our $\alpha (0)$ and $d^2\alpha (0)\mathrm{/}{d}^2{q}^2$ agree with the results of the chiral perturbation theory. The discrepancy can be traced back to the contribution of the intermediate $\mathrm{\Delta }$ state degenerate with the $N$ which is a characteristic of a large-$N_C$ model.