On the low-x behavior of nuclear shadowing

We calculate the x dependence of nuclear shadowing at moderate values of Q by using HERA diffractive data. We show that no decrease of shadowing occurs down to very low x (x ≃ 10). Also at II Facoltà di Scienze MFN, 15100 Alessandria, Italy. Supported by EU Contract ERBFMBICT950427. The possibility of studying nuclear shadowing (i.e. the depletion of bound nucleon structure functions (F 2 ) with respect to the free nucleon ones (F N 2 )) at HERA [1] has prompted new interest on this subject. Different models and interpretations have been suggested in the past years to explain nuclear shadowing [2]. A nuclear HERA program would allow extending the experimental investigation to very low x, thus offering the chance of a deeper understanding of the phenomenon. One recent interesting prediction [3] is that, at low x and for moderately large Q (Q ∼ 10 GeV) shadowing stops its rise, starts decreasing and eventually vanishes. This effect arises from the different low-x behavior of the inclusive and the diffractive structure functions. In fact, at x ≪ 1, whereas F2(x,Q ) ∼ (1/x) 2), with a ‘hard’ intercept ∆(Q) ≈ 0.3− 0.4, the shadowing term ∆F sh 2 ≡ F A 2 − F N 2 , which is proportional to the diffractive structure function, is dominated by soft physics and has an asymptotic x dependence of the form ∆F sh 2 ∼ (1/x) 2∆(μ2), with ∆(μ) ≈ 0.1, where μ is the typical scale of soft interactions. While the argument above is rather general and correct, the specific finding of Ref. [3], i.e. that at Q ∼ 10 GeV shadowing reaches its largest value already at x ≈ 10 and then begins to decrease towards smaller x, is based on some restrictive assumptions. We shall call x0 the x value where shadowing attains its maximum. The value of x0 is found in [3] to be almost independent of Q 2 (for Q ∼ > 5 GeV ) and of the atomic mass. The prediction of [3] is that in the region between x = 10 and x = 10 shadowing should be a decreasing function of x towards x → 0. It is evident that such a behavior should easily be observable at HERA. The results of Ref. [3] rely on two assumptions: 1) the shadowing term, which is related to the diffractive structure function, is given by a simple power–like parameterization ∆F sh 2 ∼ x 2−2αIP (0) (1) with αIP (0) ≃ 1.1; 2) the mass M of the diffractively produced states is kept fixed and equal to Q. Both these assumptions are questionable. The first one is true only asymptotically, as x → 0, and cannot be used to draw any conclusion about the x-region between 10