Perturbative gluon shadowing in heavy nuclei.

We study how much gluon shadowing can be perturbatively generated through the modified QCD evolution in heavy nuclei. The evolution of small-x gluons is investigated within the semiclassical approximation. The method of characteristics is used to evaluate the shadowed distributions in low-Q and small-x region. In solving the modified evolution equation, we model in simultaneously fusions from independent constituents and from the same constituent, both in a proton and in a large loosely bound nucleus of A ∼ 200. In addition to the actual distributions at small x, we study the ratios of the distributions at an initial scale Q0 = 2 GeV, and show that a strong nuclear shadowing can follow from the modified QCD evolution. ∗This work was supported by the Director, Office of Energy Research, Division of Nuclear Physics of the Office of High Energy and Nuclear Physics of the U.S. Department of Energy under Contract No. DE-AC03-76SF00098. The semihard gluonic subprocesses are expected to play an essential role in the formation of high energy densities in heavy ion collisions at collider energies [1, 2, 3, 4]. However, there are many theoretical uncertainties in modeling these QCD processes. One of the major ones, nuclear gluon shadowing, comes from the unknown initial gluon distributions at small x. Unlike for the quark and antiquark distributions, there are no direct experimental data for the gluons in nuclei. Getting theoretical control over the nuclear gluon shadowing is therefore a very urgent and important issue. The purpose of this Letter is to study how much gluonic shadowing is generated perturbatively through the modified QCD evolution [5, 6] in heavy nuclei. “Shadowing” in the context of the deep inelastic lA-scattering refers to the measured depletion of the nuclear structure function F 2 at small xBj, as compared to F2 of unbound nucleons [7]. The same kind of depletion at small x is expected to happen also in the nuclear gluon distributions. During the recent years there have been many efforts to explain the measured nuclear shadowing of quarks and antiquarks [8]-[15] but for gluons the situation is still inconclusive. Once the nuclear parton distributions are known at an initial scale Q0, the QCD-evolution to larger Q can be computed [6, 16, 17]. The problem is how to get input, theoretically or experimentally, for the nuclear gluon distributions at Q0, and to understand the reliability of QCD-evolution for the proper range of xand Q-values. Shadowing-phenomenon is also predicted to happen in protons. In this case, “shadowing” refers to the depletion of the actual parton distributions, and is caused by the fusions of overcrowding gluons at very small x. This mechanism proceeds through perturbative QCD-evolution as formulated in [5, 6]. It has been shown by Collins and Kwieciński that the singular gluon distributions actually saturate due to the fusions [18]. In this Letter our basic idea is quite straightforward. We first compute the gluon shadowing in a proton, by using techniques introduced in [18] for solving the smallx evolution including gluon recombination. Then we apply the same mechanism of recombining gluons to heavy nuclei and study to what extent nuclear shadowing is generated perturbatively through the QCD-evolution at Q0 = 2 GeV. At small values of x, leading order QCD evolution equation predicts that the number of gluons becomes extremely large. It has been known [5, 6] that for sufficiently small values of x and/or of Q, the total transverse area occupied by the gluons will be larger than the transverse area of a hadron, so that the interaction between gluons can no longer be neglected. Such gluon recombination results in a modification of the QCD evolution equations. In the limit of small-x the modified QCD evolution