Effective Action and Electromagnetic Polarizabilities of Nucleons in QCD String Theory

The effective action for baryons in the external electromagnetic fields is obtained on the basis of the QCD string theory. The area law of the Wilson loop integral, the approximation of the Nambu-Goto straight-line strings, and the asymmetric quark-diquark structure of nucleons are used to simplify the problem. The spin-orbit and spin-spin interactions of quarks are treated as a perturbation. With the help of the virial theorem we estimate the mean radii of nucleons in terms of the string tension and the Airy function zeros. On the basis of the perturbation theory in small external electromagnetic fields we derive the electromagnetic polarizabilities of nucleons. The electric and diamagnetic polarizabilities of a proton are $\bar{\alpha}_p= 10\times 10^{-4} fm^3$, $\beta_p^{dia}=-8\times 10^{-4} fm^3$ and for a neutron we find $\bar{\alpha}_n=4.2\times 10^{-4} fm^3$, $\beta_n^{dia}= -5.4\times 10^{-4} fm^3$. Reasonable values of the magnetic polarizabilities $\bar{\beta}_p=(5\pm 3)\times 10^{-4} fm^3$, $\bar{\beta}_n=(7.6\pm 3)\times 10^{-4} fm^3$ are estimated using the $\Delta$ contribution to the paramagnetic polarizability of the nucleons.