Joint ECFA-NuPECC-APPEC Workshop “Synergies between the EIC and the LHC”

Forward physics provides invaluable information for the study of
saturation in QCD. While the color-glass-condensate constitutes the
theoretical framework to study saturation within QCD, there is also a
consistent approach that allows for a perturbative factorization of
cross sections for forward production in terms of PDFs and parton-level
scattering, called Improved TMD factorization. It is valid both for LHC
and EIC physics. Furthermore, it can be formulated in momentum space and
is ideal for Monte Carlo approaches. We report on progress on the
precision of such calculations.