Determination of the anomalous dimension of gluonic operators in deep inelastic scattering at O(1/N_f)

Abstract

Using large N_f methods we compute the anomalous dimension of the predominantly gluonic flavour singlet twist-2 composite operator which arises in the operator product expansion used in deep inelastic scattering. We obtain a d-dimensional expression for it which depends on the operator moment n. Its expansion in powers of epsilon = (4-d)/2 agrees with the explicit exact three loop MSbar results available for n less than or equal to 8 and allows us to determine some new information on the explicit n-dependence of the three and higher order coefficients. In particular the n-dependence of the three loop anomalous dimension gamma_{gg}(a) is determined in the C_2(G) sector at O(1/N_f).

26 latex pages, 7 postscript figures

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• The four-loop beta-function in Quantum Chromodynamics
• Perturbative Part of the Non-Singlet Structure Function F_2 in the Large-N_F Limit

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