Binding effects and nuclear shadowing

The effects of nuclear binding on nuclear structure functions have so far been studied mainly at fixed target experiments, and there is currently much interest in obtaining a clearer understanding of this phenomenon. We use an existing dynamical model of nuclear structure functions, that gives good agreement with current data, to study this effect in a kinematical regime (low x, high Q) that can possibly be probed by an upgrade of hera at desy into a nuclear accelerator. The ratio of the structure functions of bound and free nucleons is smaller than one at x < 0.1; this has been observed previously and is called nuclear shadowing [1]. Nuclear shadowing and its scaling proporties are generally regarded as the shadowing effect arising from gluon recombinations in the partonic model. A surprising fact of the hera data is the rapid rise of the structure function F2 of the proton as x decreases. The expected shadowing effect of gluon recombinations is not visible at least down to x ∼ 10 [2]. On the other hand, one of us (WZ) [3] has pointed out that the effect of shadowing due to gluon recombinations on a steep gluon distribution will be weakened by momentum conservation; in particular, gluon fusion can be neglected in the QCD nonlinear evolution equation in the small-x region where the gluon density rises like the Lipatov x behavior. Obviously, reconsideration of the partonic shadowing model is necessary. We have thus evolved a new approach to nuclear shadowing, which explains available data without needing Glauber rescattering [4]. On the other hand, there is a strong likelihood of hera being upgraded to a nuclear accelerating machine [5]. We therefore apply our model and obtain predictions for the nuclear structure functions in the kinematical regime of the hera machine. The Model : We quickly review the model. We consider the DIS process in the Breit frame, where the exchanged virtual boson is point-like and the target consists of partons. The zcomponent of the momentum of the struck quark is flipped in the interaction. Hence, due to the uncertainty principle, a struck quark carrying a fraction x of the nucleon’s momentum, PN , during the interaction time τint = 1/ν, will be off-shell and localized longitudinally to within a potentially large distance ∆z ∼ 1/(2xPN), which may exceed the average two-nucleon separation DA for a small enough x < x0 = 1/mNDA. The struck sea quark with its parent will return to its initial position within τint if the target is a free nucleon. However, in a bound nucleon target, it can interact with other nucleons in the nucleus and so loses its energy-momentum. Since it can be randomly distributed outside the target nucleon, and interacts incoherently with the rest of the nucleus, we regard this effect as an additive (second) binding effect rather than as a Glauber rescattering. A simple way of estimating the second binding effect is to connect this new effect with the traditional binding effect, which influences the parton input distributions at the starting point, Q = μ, of the QCD evolution. At such low scales, we picture the nucleon as being composed of valence quarks, gluons, and mesonic sea quarks. For example, we identify the GRV (LO) parametrisations [6] as the input parton distributions of the free nucleon at μ = 0.23 GeV. We consider that the attractive potential describing the nuclear force arises from the exchange of scalar mesons. Hence the energy required for binding is taken away solely from the mesonic component of the nucleon, and not from its other components. We identify this with the sea quarks (and antiquarks) in the nucleon. Therefore, we assume that the nuclear binding effect only reduces the sea distributions of the nucleon at Q = μ. For a binding energy, b, per nucleon, this corresponds to the reduction of the bound nucleon sea densities from the free-nucleon value, SN(x, μ ), given by GRV at Q = μ to SA(x, μ ) = K(A)SN (x, μ ) = ( 1− 2b MN 〈SN(μ 2)〉2 )