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

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 e = (4 − d)/2 agrees with the explicit exact three-loop MS results available for n ⩽ 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 γ gg ( a) is determined in the C 2( G) sector at O(1/ N f ).