No Froissart bound from gluon saturation

In the previous work [Phys. Rev. D 66 (2002) 051502], we showed that while the nonlinear QCD evolution equation of Balitsky and Kovchegov (BK) leads to saturation of the scattering amplitude locally in impact parameter space, it does not unitarize the total cross section. This result was recently challenged by Ferreiro, Iancu, Itakura and McLerran (FIIM) who claim that the dipole–hadron cross section computed from the BK equation saturates the Froissart bound. In this comment, we point to a fundamental error in the argument of FIIM which invalidates their conclusion. We show that if the total cross section violates unitarity for a coloured scattering probe, it does so also for a colourless scattering probe.