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Gluon Structure Function of a Color Dipole in the Light-Cone Limit of Lattice QCD

We calculate the gluon structure function of a color dipole in near-light-cone SU(2) lattice QCD as a function of $x_B$. The quark and antiquark are external non-dynamical degrees of freedom which act as sources of the gluon string configuration defining the dipole. We compute the color dipole matrix element of transversal chromo-electric and chromo-magnetic field operators separated along a direction close to the light cone, the Fourier transform of which is the gluon structure function. As vacuum state in the pure glue sector, we use a variational ground state of the near-light-cone Hamiltonian. We derive a recursion relation for the gluon structure function on the lattice similar to the perturbative DGLAP equation. It depends on the number of transversal links assembling the Schwinger string of the dipole. Fixing the mean momentum fraction of the gluons to the "experimental value" in a proton, we compare our gluon structure function for a dipole state with four links with the NLO \emph{MRST} 2002 and the \emph{CTEQAB-0} parameterizations at $Q^2=1.5 \mathrm{GeV}^2$. Within the systematic uncertainty we find rather good agreement. We also discuss the low $x_B$ behavior of the gluon structure function in our model calculation.