Triumvirate of running couplings in small-x evolution

We study the inclusion of running coupling corrections into the non-linear small-x JIMWLK and BK evolution equations by resumming all powers of alpha N-s(f). in the evolution kernels. We demonstrate that the running coupling corrections are included in the JIMWLK/BK evolution kernel by replacing the fixed coupling constant alpha(s) in it with alpha(s)(1/r(1)(2))alpha(s)(1/r(2)(2)) / alpha(s)(1/R-2), where r(1) and r(2) are transverse distances between the emitted gluon and the harder gluon (or quark) off of which it was emitted to the left and to the fight of the interaction with the target. In the formalism of Mueller's dipole model r(1) and r(2) are the transverse sizes of daughter dipoles produced in one step of the dipole evolution. The scale R is a function of two-dimensional vectors r(1) and r(2), the exact form of which is scheme-dependent. We propose using a particular scheme which gives us R as an explicit function of r(1) and r(2). (c) 2006 Elsevier B.V. All rights reserved.