An anomalous dimension for small x evolution

We construct an anomalous dimension for small x evolution which goes beyond standard fixed order perturbative evolution by including resummed small x logarithms deduced from the leading order BFKL equation with running coupling. Surprisingly, we find that once running coupling effects are properly taken into account, the leading approximation is very close to standard perturbative evolution in the range of x accessible at HERA, in overall agreement with the data, with no need for phenomenological parameters to summarise subleading effects. We also show that further corrections due to subleading small x logarithms derived from the Fadin-Lipatov kernel can be kept under control, but that they involve substantial resummation ambiguities which limit their practical usefulness.