Why Cronin Effect Happens? I'm looking for explanation on Cronin effect but unfortunately there's no Wikipedia entry or self-contained paper to start from. The statement of this effect is that:

"At leading order, multiple scattering only affect the momentum
  distribution of the final particles, but not their total number. The
  suppression at small p is compensated by an increase at larger p."

Can someone please explain why? I'm looking for a calculation based answer and not just qualitative discussion. 
 A: It looks like the following article is relevant: http://arxiv.org/abs/hep-ph/0402256 (published in Nucl. Phys. A). (The phrase you quote is probably from lectures http://www.physik.uni-bielefeld.de/~borghini/Teaching/HIC-Seminar/SoSe2013/Francois_SPhT2006-1.pdf by one of the authors of the article):

"The Cronin effect was discovered in proton-nucleus collisions in the
  late 70's[62-64]. The effect observed was a hardening of the
  transverse momentum spectrum in proton-nucleus collisions, relative to
  proton-proton collisions, that sets in at transverse momenta of order
  $k_\perp \sim 1-2$~GeV, and disappears at much larger $k_\perp$'s. A
  corresponding depletion was seen at low transverse momenta,
  accompanied by a softening of the spectrum. At that time, and indeed
  subsequently, the effect was interpreted as arising from the multiple
  scatterings of partons from the proton off partons from the nucleus
  [65]. As a result of such scatterings, the partons acquire a
  transverse momentum kick, shifting their momenta from lower to higher
  values, hereby causing the observed respective depletion and
  enhancement. At high $k_\perp$, the higher twist effects, which, in
  the language of perturbative QCD, are responsible for multiple
  scattering[66,67] are suppressed by powers of $k_\perp$.  The relative
  enhancement of the cross-sections at moderate $k_\perp$'s should thus
  die away -- and indeed, the data seemed to suggest as much.  Though a
  qualitative understanding of the previously observed Cronin effect was
  suggested by perturbative QCD, a quantitative agreement for all its
  features (such as, for instance, the flavor dependence) is still
  lacking."

The words "At leading order" in the phrase you quote suggests that this is a result of calculations. It looks like the following article is relevant: http://arxiv.org/abs/hep-ph/0201311v1.pdf :"the leading twist contribution always consists of one hard scattering on the parton level". This is almost exactly what is said in the phrase you quote. So maybe you should find out more about this "twist expansion". Probably, the phrase is about the leading order of this expansion.
A: 
Usually, Cronin effect is given in terms of the central-to-peripheral
  nuclear modification factor for $dAu$ collisions at midrapidity
$$   R^h_{CP}(p_t)=
> \frac{(1/N^C_{coll})dN^h/p_tdp_t(C)}{(1/N^P_{coll})dN^h/p_tdp_t(P)} $$
where $C$ central, $P$ reipheral, $N_{coll}$ the average number of
  inelastic $NN$ collisions.If hadronization is by fragmentation, which
  is a factorizable subprocess, the FFs for any given $h$ should cancel
  in the ratio of desribed equation, so $R^h_{CP}$ should be independent of
  h. 
However, the data show that $R^p_{CP}(p_T)>R^{\pi}_{cp}(p_T)$ for all
  $p_T$ > 1 GeV/c, when C = 0–20% and P = 60–90% centralities.
Clearly, initial-state interaction  is not able to explain this phenomenon, 
  which strongly suggests the medium-dependence of hadronization. The data further
  indicate that the $p_T$ dependence of $R^h_{CP}(p_T)$ peaks at $p_T$ ∼
  3 GeV/c for both $p$ and $\pi$, reminiscent of the $p/\pi$ ratio at
  fixed centrality in $A_uA_u$ collisions although the $C/P$ ratio for
  $dAu$ collisions is distinctly different.

"Quark-gluon Plasma 4" by Rudolph C. Hwa , 2010, p. 279
FF - fragmentation function - generally, FF is treated as a black box with a
parton going in and a hadron going out, whereas in the recombination model(RM) we open up the black box and treat the outgoing hadron as the product of recombination of shower partons, whose distributions are to be determined from the FFs.
