Anomalous Dimension of Non-Singlet Wilson Operators at O(1/N_f) in Deep Inelastic Scattering

Abstract

We use the large N_f self consistency formalism to compute the $O(1/N_f)$ critical exponent corresponding to the renormalization of the flavour non-singlet twist two Wilson operators which arise in the operator product expansion of currents in deep inelastic processes. Expanding the $d$-dimensional expression in powers of $ϵ$ $=$ $(4-d)/2$ the coefficients of $ϵ$ agree with the known two loop structure of the corresponding renormalization group function and we deduce analytic expressions for all moments, $n$, at three and higher orders in perturbation theory in the $\overline{\text{mbox}MS}$ scheme at $O(1/N_f)$.

Comments: 13 Latex pages, 1 figure (available from author on request), LTH-322