Generalized polarizabilities of the nucleon studied in the linear sigma model ( II )

In a previous paper virtual Compton scattering off the nucleon has been investigated in the one–loop approximation of the linear sigma model in order to determine the 3 scalar generalized polarizabilities. We have now extended this work and calculated the 7 vector polarizabilities showing up in the spin–dependent amplitude of virtual Compton scattering. The results fulfill 3 model–independent constraints recently derived. Compared to the constituent quark model there exist enormous differences for some of the vector polarizabilities. At vanishing three–momentum of the virtual photon, the analytical results of the sigma model and of chiral perturbation theory can be related. The influence of the π0 exchange in the t channel has been discussed in some detail. Besides, the vector polarizabilities determine 2 linear combinations of the third order spin–polarizabilities appearing in real Compton scattering.