Solution of Twist-3 Evolution Equation in Double Logarithmic Approximation in Qcd

The solution of DGLAP evolution equation for the twist-3 gluon operators is obtained in the Double Logarithmic Approximation of QCD perturbation theory. The method used for the solution is similar to the reggeon field theory. The asymptotics of the twist-3 parton correlation function for the small Bjorken variables xB is found. 1. The growth of the structure function f(xB, Q ) in the region of small Bjorken variables xB makes it necessary to take into account the high twist contribution. According to the operator product expansion the local operator of spin J contributes to the number J Mellin moment of the structure function f(xB, Q ). The Q-dependence of the operators is perturbatively determined by evolution equation collecting in the leading order (LLA) the terms of the form (αS lnQ /μ). The asymptotic behavior for xB → 0 is governed by the rightmost singularity of the anomalous dimension in the variable J continued to the complex plane. However the calculation of the anomalous dimension becomes more complicated for twists N ≥ 3 because of the large number of the local operators. There is another approach proposed in Ref.[1] and based on the relation of small-xB behavior of the structure function and BFKL equation summing up the powers (αS ln 1/xB) . It enables to find twist-2 anomalous dimension near the singularity position J → 1 for the leading and next to leadings orders in terms of lnQ. The situation is also more involved for the higher twists N ≥ 3 since one has to solve the equation for N reggeized gluons [2] and then to extract from it the anomalous dimension. 2. Here we consider the evolution equation for the twist-3 quasipartonic operators in double logarithmic approximation (DLA), which collects the