Anomalous Dimensions of High Twist Operators in QCD at $N \rightarrow 1$ and large $Q^2

Abstract

The anomalous dimensions of high-twist operators in deeply inelastic scattering ($γ_{2n}$) are calculated in the limit when the moment variable $N \rightarrow 1$ (or $x_B\rightarrow 0$) and at large $Q^2$ (the double logarithmic approximation) in perturbative QCD. We find that the value of $γ_{2n}(N-1)$ in this approximation behaves as ${N_c α_S \over π(N-1)} n^2(1 + {δ\over 3} (n^2-1))$ where $δ\approx 10^{-2}$. This implies that the contributions of the high-twist operators give rise to an earlier onset of shadowing than was estimated before. The derivation makes use of a Pomeron exchange approximation, with the Pomerons interacting attractively. We find that they behave as a system of fermions.