Unified QCD Evolution Equations and the Dominant Behaviour of Structure Functions at Low X

Abstract

We consider a system of evolution equations for quark and gluon structure functions satisfying the leading-logarithmic behaviour due to both QCD collinear $ \left(LLQ^2 \right) $ and infrared $ (LL1/x) $ singularities. We show that these equations leave undetermined an arbitrary regular function of $j$ in the Mellin-transformed weights. We consider the constraints resulting from energy-momentum conservation and from the decoupling of quark loops in the leading $ j $-plane singularity. These constraints can be fulfilled without influencing the leading-log terms. As a particular consequence of the second constraint, the location of the leading singularity is determined in terms of the $ (LL1/x) $ and $ \left(LLQ^2 \right) $ kernels. It leads to a value significantly lower than the $ LL1/x $ evaluation, while remaining at $j > 1,$ and compatible with the behaviour of structure functions observed at HERA.