Tachyon dynamics of the black disc limit in the hard small $x$ processes   in QCD
  We investigate the effective field theory (EFT) which gives the approximate description of the scattering of the two hard small dipoles in the small $x$ processes in QCD near the black disc limit(BDL). We argue that the perturbative QCD approaches predict the existence of tachyon and visualize it in the approximation where $\alpha'_P=0$ . We demonstrate that the high energy behavior of the cross-section depends strongly on the diffusion law in the impact parameter plane. On the other hand, almost threshold behavior of the cross section of the hard processes and multiplicities, i.e. fast increase of cross sections (color inflation), melting of ladders into color network and softening of the longitudinal distributions of hadrons are qualitatively insensitive to the value of diffusion in the impact parameter space. We evaluate $\alpha'_P$ near the black disk limit and find significant $\alpha'_P$ as the consequence of the probability conservation. 
B.Blok and L. Frankfurt