  We present an analysis of data on single inclusive pion production measured
by the LHCf collaboration in high-energy proton-proton and proton-nucleus at
ultra-forward rapidities, $8.8 \leq\! y\leq \!10.8$. We also analyse forward
RHIC data for calibration purposes. Our analysis relies on the use of a Monte
Carlo event generator that combines a perturbative description of the
elementary scattering process at partonic level based on the hybrid formalism
of the Color Glass Condensate with an implementation of hadronization in the
framework of the Lund string fragmentation model. This procedure allows us to
reach values of the momenta of the produced particles as low as detected
experimentally $p_t\sim0.1$ GeV. We achieve a good description of single
inclusive spectra of charged particles and neutral pions at RHIC and the LHC
respectively, and nuclear modification factors for proton-lead collisions at
the LHC. Our results add evidence to the idea that particle production in the
domain of very small Bjorken-$x$ is dominated by the saturation effects encoded
in the unintegrated gluon distribution of the target. Being forward particle
production of key importance in the development of air showers, we stress that
this approach allows for a theoretically controlled extrapolation of our
results to the scale of ultra-high energy cosmic rays, thus serving as starting
point for future works on this topic.
