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 $\left(LLQ^2 \right)$ 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.