Nuclear Attenuation in Hard Processes

Nonexponential attenuation of hadrons in nuclei and renormalization of data for hard QCD probes. For classical particles the propagation through a medium is exponentially attenuated with the path length L, i.e. the survival probability in a nucleus decreases as exp(−σhN in ρL), where σ in is the cross section of inelastic hadron-nucleon collisions, and ρ is the nuclear density. This kind of attenuation is actually what the Glauber model is based upon. However, it is known since Gribov’s work [1] that this behavior is subject to quantum corrections. The incoming hadron experiences quantum fluctuations which make the medium more transparent [2]. For QCD, gauge invariance leads to the phenomenon of color transparency [3, 4] which means that small size fluctuations have a cross section which vanishes quadratically with their transverse dimension. As a result, the dependence of the attenuation factor on L changes from an exponential to a power in L [3]. Thus, the Glauber model predicts corrections known as Gribov’s inelastic shadowing. A deviation of the Glauber model calculations from data by about 10% has been well established experimentally up to the energy 280 GeV in the nuclear rest frame. It is a theoretical challenge to predict Gribov’s corrections at the energies of RHIC and LHC which are two and five orders of magnitude higher, respectively. In experiments studying heavy ion and proton-nucleus collisions the Glauber model is widely used for calculation of inelastic cross sections, the so called number of collisions, the number of participants, etc. The current normalization of data for the cross sections of hard processes (high-pT , heavy flavors, etc.) relies on Glauber model calculations and therefore should be corrected accordingly. The problem of calculating the inelastic shadowing corrections in all orders for multiple interactions was solved in [2] using the light-cone dipole approach. The impact parameter dependence of Gribov’s corrections to the inelastic deuteron-gold cross section is shown in Fig. 1. Together with a correction for missed diffractive events in the tagged minimal bias event sample of PHENIX, this amounts to about 20% reduction of all hard reaction cross sections, which is of the same order of magnitude as the detected effects (the Cronin enhancement in high-pT production, nuclear suppression of J/Ψ and open charm). The lack of inelastic shadowing corrections in the analyses of experimental data can mimic real effects, as is demonstrated for a few examples below. Frequently nuclear effects are studied comparing peripheral and central collisions. In such a case the cross sections are normalized to the number of collisions calculated in the Glauber model. In this case inelastic shadowing corrections affect the ratio much more than in the minimal bias case. Indeed, according to Fig. 1 these corrections are hardly visible in the nuclear center, while they reach a maximum of about 30-40% at the nuclear periphery. This could explain at least part of the unusually large Cronin 0 0.2 0.4 0.6 0.8 1