Collective Phenomena in $pp$ and $ep$ Scattering
  Bjorken scaling violation in deep inelastic electron-proton scattering (DIS) is related to the rise of hadronic cross sections by using the additive quark model. Of special interest is the connection between saturation in the low-$x$ behavior of the DIS structure functions (SF) and possible slow-down of the $pp$ cross section rise due to saturation effects. We also identify saturation effects in the DIS SF with phase transition that can be described by the Van der Waals equation of state. 
Francesco Giovanni Celiberto, Roberto Fiore, L\'aszl\'o Jenkovszky
hep-ph