The 3-loop QCD calculation of the moments of deep inelastic structure functions

Abstract: We present the analytic next-to-next-to-leading perturbative QCD corrections in the leading twist approximation for the moments N=2,4,6,8 of the flavour singlet deep inelastic structure functions F_2 and F_L. We calculate the three-loop anomalous dimensions of the corresponding singlet operators and the three-loop coefficient functions of the structure functions F_L and F_2. In addition, we obtained the 10th moment for the non-singlet structure functions in the same order of perturbative QCD. We perform an analysis of the obtained results.