Renormalization of Twist-4 Operators in QCD Bjorken and Ellis-Jaffe Sum Rules

The QCD effects of twist-4 operators on the first moment of nucleon spin-dependent structure function $g_1(x, Q^2 )$ are studied in the framework of operator product expansion and renormalization group method. We investigate the operator mixing through renormalization of the twist-4 operators including those proportional to the equation of motion by evaluating off-shell Green's functions in the usual covariant gauge as well as in the background gauge. Through this procedure we extract the one-loop anomalous dimension of the spin 1 and twist-4 operator which determines the logarithmic correction to the $1/Q^2$ behavior of the contribution from the twist-4 operators to the first moment of $g_1(x,Q^2)$.