Color Glass Condensate in Brane Models or Don't Ultra High Energy Cosmic Rays Probe 1015eV10^{15}eV Scale ?

In a previous work hep-ph/0203165 we have studied propagation of relativistic particles in the bulk for some of most popular brane models. Constraints have been put on the parameter space of these models by calculating the time delay due to propagation in the bulk of particles created during the interaction of Ultra High Energy Cosmic Rays with protons in the terrestrial atmosphere. The question was however raised that probability of hard processes in which bulk modes can be produced is small and consequently, the tiny flux of UHECRs can not constrain brane models. Here we use Color Glass Condensate (CGC) model to show that effects of extra dimensions are visible not only in hard processes when the incoming particle hits a massive Kaluza-Klein mode but also through the modification of soft/semi-hard parton distribution. At classical level, for an observer in the CM frame of UHECR and atmospheric hadrons, color charge sources are contracted to a thin sheet with a width inversely proportional to the energy of the ultra energetic cosmic ray hadron and consequently they can see an extra dimension with comparable size. Due to QCD interaction a short life swarm of partons is produced in front of the sheet and its partons can penetrate to the extra-dimension bulk. This reduces the effective density of partons on the brane or in a classical view creates a delay in the arrival of the most energetic particles if they are reflected back due to the warping of the bulk. In CGC approximation the density of swarm at different distance from the classical sheet can be related and therefore it is possible (at least formally) to determine the relative fraction of partons in the bulk and on the brane at different scales. Results of this work are also relevant to the test of brane models in hadron colliders like LHC.Comment: 17 pages, 3 figures. Text is modified to highlight the relation between the distribution gluons at high and low rapidity scales. v3: published versio

On the behaviour of single scale hard small xx processes in QCD near the black disc limit

We argue that at sufficiently small Bjorken $x$ where pQCD amplitude rapidly increases with energy and violates probability conservation the shadowing effects in the single-scale small $x$ hard QCD processes can be described by an effective quantum field theory of interacting quasiparticles. The quasiparticles are the perturbative QCD ladders. We find, within the WKB approximation, that the smallness of the QCD coupling constant ensures the hierarchy among many-quasiparticle interactions evaluated within physical vacuum and in particular, the dominance in the Lagrangian of the triple quasiparticle interaction. It is explained that the effective field theory considered near the perturbative QCD vacuum contains a tachyon relevant for the divergency of the perturbative QCD series at sufficiently small $x$. We solve the equations of motion of the effective field theory within the WKB approximation and find the physical vacuum and the transitions between the false (perturbative) and physical vacua. Classical solutions which dominate transitions between the false and physical vacua are kinks that cannot be decomposed into perturbative series over the powers of $\alpha_s$. These kinks lead to color inflation and the Bose-Einstein condensation of quasiparticles. The account of the quantum fluctuations around the WKB solution reveals the appearance of the "massless" particles-- "phonons". It is explained that "phonons" are relevant for the black disc behaviour of small $x$ processes, leading to a Froissart rise of the cross-section. The condensation of the ladders produces a color network occupying a "macroscopic" longitudinal volume. We discuss briefly the possible detection of new QCD effects.Comment: 24 pages, 1 Figure. References added, and several misprints eliminate