Perturbatively stable resummed small x evolution kernels

We present a small x resummation for the GLAP anomalous dimension and its corresponding dual BFKL kernel, which includes all the available perturbative information and non-perturbative constraints. Specifically, it includes all the information coming from next-to-leading order GLAP anomalous dimensions and BFKL kernels, from the constraints of momentum conservation, from renormalization-group improvement of the running coupling and from gluon interchange symmetry. The ensuing evolution kernel has a uniformly stable perturbative expansion. It is very close to the unresummed NLO GLAP kernel in most of the HERA kinematic region, the small x BFKL behaviour being softened by momentum conservation and the running of the coupling. Next-to-leading corrections are small thanks to the constraint of gluon interchange symmetry. This result subsumes all previous resummations in that it combines optimally all the information contained in them.