Unified QCD evolution equations and the dominant behaviour of structure functions at low x

We consider a system of evolution equations for quark and gluon structure functions satisfying the leading-logarithmic behaviour due to both QCD collinear (LLQ2) 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 (LLQ2) 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.