In a previous work
we have studied the propagation of relativistic particles
in the bulk for some of the 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 (UHECRs)
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 cannot 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 photon/parton 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 distances 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.