Saturating Cronin effect in ultrarelativistic proton-nucleus collisions

Experimental results on pion and photon production in high-energy hadron-nucleus collisions show an extra increase at high transverse momentum (pT ) over what would be expected based on a simple scaling of the appropriate proton-proton (pp) cross sections. The nuclear enhancement is referred to as the Cronin effect [1], and is most relevant at moderate transverse momenta (3 GeV ∼ pT ∼ 6 GeV) [2]. In relativistic nuclear collisions this momentum region is at the upper edge of the pT window in Super Proton Synchrotron (SPS) experiments at √ s = 20 AGeV, and is measurable at the Relativistic Heavy Ion Collider (RHIC) at √ s = 200 AGeV. The importance of a better theoretical understanding of the Cronin effect continues to increase [3–5] as new data appear from the SPS heavy-ion program and as the commissioning of RHIC approaches. This calls for a systematic study of particle production moving from pp to protonnucleus (pA) collisions. In the present work we analyze the Cronin effect in inclusive π and γ production. In the past two decades the perturbative QCD (pQCD) improved parton model has become the description of choice for hadronic collisions at large pT . The pQCD treatment of hadronic collisions is based on the assumption that the composite structure of hadrons is revealed at high energies, and the parton constituents become the appropriate degrees of freedom for the description of the interaction at these energies. The partonic cross sections are calculable in pQCD at high energy to leading order (LO) or next-to-leading-order (NLO) [6–8]. The parton distribution function (PDF) and the parton fragmentation function (FF), however, require the knowledge of non-perturbative QCD and are not calculable directly by present techniques. The PDFs and FFs, which are believed to be universal, are fitted to reproduce the data obtained in different reactions. In recent NLO calculations the various scales (Q,ΛQCD, etc.) are optimized to improve the agreement between data and theory [9,10]. In theoretical investigations of π and γ production in pA collisions another method appeared and became popular [11–13]: the different scales of the pQCD calculations are fixed and the NLO pQCD theory is supplemented by an additional non-perturbative parameter, the intrinsic transverse momentum (kT ) of the partons. The presence of an intrinsic transverse momentum, as a Gaussian type broadening of the transverse momentum distribution of the initial state partons in colliding hadrons was investigated as soon as pQCD calculations were applied to reproduce large-pT hadron production [14,15]. The average intrinsic transverse momentum needed was small, 〈kT 〉 ∼ 0.3− 0.4 GeV, and could be easily understood in terms of the Heisenberg uncertainty relation for partons inside the proton. This simple physical interpretation was ruled out as the only source of intrinsic kT by the analysis of new experiments on direct photon production, where 〈kT 〉 ∼ 1 GeV was obtained in the fix target Tevatron experiments [11–13] and 〈kT 〉 ∼ 4 GeV was found at the Tevatron collider for muon, photon and jet production [13]. New theoretical efforts were ignited to understand the physical origin of 〈kT 〉 [16,17]. Parallel to these developments, kT smearing was applied successfully to describe ultrarelativistic nucleus-nucleus collisions [3,4] and J/ψ production at Tevatron and HERA [18]. One possible explanation of the enhanced kT -broadening is in terms of multiple gluon radiation [17], which makes 〈kT 〉 reaction and energy dependent. In the absence of a full theoretical description, intrinsic kT can be used phenomenologically in pp collisions. A reasonable reproduction of the pp data is a prerequisite for the isolation of the nuclear enhancement we intend to focus on. In the lowest-order pQCD parton model, direct pion production can be described in pp collisions by