Small-x Resummations for the Structure Functions F

The numerical effects of the known all-order leading and next-toleading logarithmic small-x contributions to the anomalous dimensions and coefficient functions of the unpolarized singlet evolution are discussed for the structure functions F ep 2 (x, Q ), F ep L (x, Q ), and F eγ 2 (x, Q ). Introduction The evolution kernels of the deep-inelastic scattering (DIS) structure functions contain large logarithmic contributions for small Bjorken-x. The effect of resumming these terms to all orders in αs can be consistently studied in a framework based on the renormalization group (RG) equations, which describes the mass factorization. In this framework, the evolution equations of fixed-order perturbative QCD are generalized by including the resummed small-x contributions to the respective anomalous dimensions andWilson coefficients [1–4] beyond next-to-leading order in αs (NLO). The numerical impact of these higher-order contributions has been investigated for the non-singlet nucleon structure functions F p−n 2 and F νN 3 [5], g p−n 1 [5,6] and g γZ 5 [7]; for the polarized singlet quantity g p 1,S [8], and for the unpolarized singlet structure functions F2,S [9–11] and F p L,S [10]. F p 2,S and F p L,S have been studied using different RG-based approaches as well [12]. In the present note we extend a previous account [7] by considering, besides the resummed next-to-leading logarithmic small-x (NLx) quark terms of ref. [2], also the recently derived NLx contributions ∝ Nf to the anomalous 1) Talk presented by J. Blümlein. To appear in: Proceedings of the 5th International Workshop on Deep Inelastic Scattering and QCD (DIS 97), Chicago, April 1997 c © 1997 American Institute of Physics 1