Structure function and angular ordering at small x

Abstract

We compute the gluon distribution in deep inelastic scattering at small x by solving numerically the angular ordering evolution equation. The leading-order contribution, obtained by neglecting angular ordering, satisfies the BFKL equation. Our aim is the analysis of the subleading corrections. Although not complete — the exact next-to-leading contribution is not yet available — these corrections are important since they come from the physical property of coherence of QCD radiation. In particular we discuss the subleading correction to the BFKL characteristic function and the gluon distribution's dependence on the maximum available angle. Conformal invariance of the BFKL equation is lost, however this is not enough to bring the small- x gluon distribution into the perturbative regime: although large momentum regions are enhanced by angular ordering, the small momentum regions are not fully suppressed. As a consequence the gluon anomalous dimension is finite and tends to the BFKL value γ = 1 2 for α s → 0 . The main physical differences with respect to the BFKL case are that angular ordering leads to (1) a larger gluon anomalous dimension, (2) less singular behaviour for x → 0 and (3) reduced diffusion in transverse momentum.