It is known that multiple partonic scatterings in high-energy proton-proton
(
pp) collisions must happen in parallel. However, a rigorous parallel
scattering formalism, taking energy sharing properly into account, fails to
reproduce factorization, which on the other hand is the basis of almost all
pp event generators. In addition, binary scaling in nuclear scatterings is
badly violated. These problems are usually ``solved'' by simply not considering
strictly parallel scatterings, which is not a solution. I will report on new
ideas (leading to EPOS4), which allow recovering perfectly factorization, and
also binary scaling in
AA collisions, in a rigorous unbiased parallel
scattering formalism. In this new approach, dynamical saturation scales play a
crucial role, and this seems to be the missing piece needed to reconcile
parallel scattering with factorization. From a practical point of view, one can
compute within the EPOS4 framework parton distribution functions (EPOS PDFs)
and use them to compute inclusive
pp cross sections. So, for the first time,
one may compute inclusive jet production (for heavy or light flavors) at very
high transverse momentum (
pt) and at the same time in the same formalism
study flow effects at low
pt in high-multiplicity
pp events, making
EPOS4 a full-scale ``general purpose event generator''. I discuss applications,
essentially multiplicity dependencies (of particle ratios, mean
pt, charm
production) which are very strongly affected by the saturation issues discussed
in this paper.