Running coupling and power corrections in non-linear evolution at the high-energy limit

A main feature of high-energy scattering in QCD is saturation in the number density of gluons. This phenomenon is described by non-linear evolution equations, JIMWLK and BK, which have been derived at leading logarithmic accuracy. In this paper we generalize this framework to include running coupling corrections to the evolution kernel. We develop a dispersive representation of the dressed gluon propagator in the background of Weiszäcker–Williams fields and use it to compute corrections to the kernel to all orders in perturbation theory. The resummed kernels present infrared-renormalon ambiguities, which are indicative of the form and importance of non-perturbative power corrections. We investigate numerically the effect of the newly computed perturbative corrections as well as the power corrections on the evolution. We present numerical results for the evolution rate as a function of the saturation scale. We find that running-coupling corrections are necessary for making quantitative predictions even when the saturation scale is very large; at present energies also the power corrections are important.