Triumvirate of Running Couplings in Small-x Evolution

Abstract

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_s N_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 right 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.