Cronin effect and energy conservation constraints in high energy proton-nucleus collisions

We estimate the Cronin effect in pA collisions at the CERN LHC and at the BNL RHIC, using a Glauber-eikonal model of initial state multiparton interactions. For a correct determination of the initial parton flux, we upgrade the model cross section, taking carefully into account all kinematical constraints of each multiparton interaction process. As compared with previous results, derived with approximate kinematics, we obtain a softer spectrum of produced partons, while improving the agreement of the model with the recent measurements of ${\ensuremath{\pi}}^{0}$ production in $d+\mathrm{Au}$ collisions at $\sqrt{s}=200A\mathrm{GeV}.$