Unified QCD evolution equations for quarks and gluons

Abstract

Considering the BFKL and DGLAP QCD evolution equations for structure functions, we discuss the possibility of unifying them in the whole $x$ and $Q^2$ range. We emphasize that the main problem is related to the constraint of angular ordering of the radiation, and the cancellation of the related collinear singularities for inclusive processes. At the leading log\ $1/x$ and log\ $Q^2$ level, we write down a unified system of equations satisfying this cancellation constraint. At low $x$, it leads to a less singular behaviour of the structure functions than the BFKL prediction.