  Average transverse momentum of hadrons produced in high energy collisions is
proposed as a diagnostic probe of high density (saturation) physics. We show
that by introducing and varying a transverse momentum cutoff in the definition
of the average transverse momentum, one can eliminate the uncertainty in the
overall magnitude of the leading order hadron production cross section in high
energy collisions, and semi-quantitatively map the different dynamical regions
predicted by the saturation physics. We discuss the applications of this method
to pion production at RHIC and LHC and make quantitative predictions for the
average transverse momentum of produced pions in the kinematics appropriate for
the RHIC and LHC experiments.
