On the running coupling in the JIMWLK equation

We propose a new method to implement the running coupling constant in the JIMWLK equation, imposing the scale dependence on the correlation function of the random noise in the Langevin formulation. We interpret this scale choice as the transverse momentum of the emitted gluon in one step of the evolution and show that it is related to the "Balitsky" prescription for the BK equation. This slows down the evolution speed of a practical solution of the JIMWLK equation, bringing it closer to the x-dependence inferred from fits to HERA data. We further study our proposal by a numerical comparison of the BK and JIMWLK equations.Comment: 13 pages, 11 figures, RevTe