Non-linear QCD evolution with improved triple-pomeron vertices

In a previous publication, we have constructed a set of non-linear evolution equations for dipole scattering amplitudes in QCD at high energy, which extends the Balitsky–JIMWLK hierarchy by including the effects of fluctuations in the gluon number. In doing so, we have relied on the color dipole picture, and we have neglected the non-locality of the two-gluon exchanges in the relation between scattering amplitudes and dipole densities. In this Letter, we relax the latter approximation, and thus restore the correct structure of the ‘triple-pomeron vertex’ which describes the splitting of one BFKL pomeron into two in the terms responsible for fluctuations. The ensuing triple-pomeron vertex coincides with the one previously derived by Braun and Vacca within perturbative QCD. The evolution equations can be recast in a Langevin form, but with a multivariable noise term with off-diagonal correlations. Our equations are shown to be equivalent with the modified version of the JIMWLK equation recently proposed by Mueller, Shoshi, and Wong.