Universality of QCD Traveling Waves with Running Coupling

The BFKL equation [1] is known to provide an incomplete description of the hadronic or nuclear collisions in the the high energy limit of QCD. That evolution equation relies indeed on the assumption of a dilute partonic content of incoming particles, but it inevitably leads to denser and denser ones. It also violates the Froissart bound and therefore unitarity. At high density, and hence at very high energy, coherent collective effects modify the BFKL equation by reducing the emission of additional soft gluons. That mechanism of gluon saturation tames the BFKL growth of the cross sections, and is expected to restore unitarity. Several evolution equations with saturation have been derived, like the B-JIMWLK [2, 3] or the BK [2, 4] equations, implementing nonlinear effects on top of the BFKL equation. However, the result discussed here is independent of the precise saturation mechanism at work. The features of gluon saturation are well known at the leading logarithmic accuracy (LL) with fixed QCD coupling. The saturation scale Qs(Y ), which is the typical momentum scale for the onset of nonlinear effects, is related to the color correlation length in the transverse plane. Hence, that