Effective Actions, Radii and Electromagnetic Polarizabilities of Hadrons in QCD String Theory

Abstract

A nonperturbative approach to QCD describing confinement and chiral symmetry breaking is discussed. It is based on the path integral representation of Green's function of quarks and leads to the QCD string theory. The effective actions for mesons and baryons in the external uniform static electromagnetic fields are obtained. The area law of the Wilson loop integral, the approximation of the Nambu-Goto straight-line string, 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. Using the virial theorem we estimate the mean radii of hadrons 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 $, $\beta_n^{dia}= -5.4\times 10^{-4} fm^3$. Using the $\Delta$ contribution to the paramagnetic polarizability of the nucleons, 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.