Angular ordering and small - x structure functions

This talks examines the effect of angular ordering on the small-x evolution of the unintegrated gluon distribution, and discusses the characteristic function for the CCFM equation. For some time now it has been known that angular ordering [1] is an essential element in any description of small-x final state properties [2]. As a first step of a programme to study the final state in small-x physics, one should examine the effect of angular ordering on the small-x evolution of the gluon structure function. Phenomenological studies have already been performed [3], but this talk will examine the solutions of the CCFM equation [2] from a more theoretical point of view. The main difference between the BFKL [4] and CCFM equations is in the collinear region: in the BFKL case, the i emission has transverse momentum qi > μ, with μ → 0; this regulates the collinear divergence which is present, but gives the wrong final state properties. In the CCFM case, angular ordering of emissions leads to the following condition (see figure 1): θi > θi−1 , ⇒ qi > zi−1qi−1 , with the corresponding gluon emission distribution being dPi = dqi πq i dzi ᾱS zi ∆(zi, qi, ki) Θ(qi − zi−1qi−1) . The non-Sudakov form factor ∆, which is analogous to a probability for suppressing any further radiation, is defined by ln∆(zi, qi, ki) = − ∫ 1 zi dz′ ᾱS z ∫ dq q′2 Θ(ki − q ′) Θ(q′ − z′qi) . c © 1997 American Institute of Physics 1