The scale dependent nuclear effects in parton distributions for practical applications

The scale dependence of the ratios of parton distributions in a proton of a nucleus $A$ and in the free proton, $R_i^A(x,Q^2)=f_{i/A}(x,Q^2)/f_i(x,Q^2)$, is studied within the framework of the lowest order leading-twist DGLAP evolution. By evolving the initial nuclear distributions obtained with the GRV-LO and CTEQ4L sets at a scale $Q_0^2$, we show that the ratios $R_i^A(x,Q^2)$ are only moderately sensitive to the choice of a specific modern set of free parton distributions. We propose that to a good first approximation, this parton distribution set-dependence of the nuclear ratios $R_i^A(x,Q^2)$ can be neglected in practical applications. With this result, we offer a numerical parametrization of $R_i^A(x,Q^2)$ for all parton flavours $i$ in any $A>2$, and at any $10^{-6}\le x \le 1$ and any $Q^2\ge 2.25$ GeV$^2$ for computing cross sections of hard processes in nuclear collisions.Comment: 14 pages, including 4 eps-figure

Constraints for nuclear gluon shadowing from DIS data

The $Q^2$ dependence of the ratios of the cross sections of deep inelastic lepton--nucleus scattering is studied in the framework of leading twist, lowest order perturbative QCD. The $\log Q^2$ slope of the ratio $F_2^{\rm Sn}/F_2^{\rm C}$ is computed by using the DGLAP evolution equations, and shown to be sensitive to the nuclear gluon distribution functions. Four different parametrizations for the nuclear effects of parton distributions are studied. We show that the NMC data on the $Q^2$ dependence of $F_2^{\rm Sn}/F_2^{\rm C}$ rule out the case where nuclear shadowing (suppression) of gluons at $x\sim 0.01$ is much larger than the shadowing observed in the ratio $F_2^A/F_2^{\rm D}$. We also show that the possible nonlinear correction terms due to gluon fusion in the evolution equations do not change this conclusion. Some consequences for computation of RHIC multiplicities, which probe the region x\gsim0.01, are also discussed.Comment: 11 pages, 3 eps figure

Constraints for nuclear gluon densities from DIS data

The $Q^2$ dependence of the ratios of nuclear structure functions $F_2^A$ is studied by performing QCD evolution of nuclear parton distribution functions. The log $Q^2$ slope of these ratios is very sensitive to the nuclear gluon distribution function. Taking different parametrizations, we show that the NMC data on the $Q^2$ dependence of $F_2^{\rm Sn}/F_2^{\rm C}$ rule out the case where nuclear shadowing (suppression) of gluons at $x\sim 0.01$ is much larger than the shadowing observed in the ratio $F_2^A/F_2^{\rm D}$. We also take into account modifications to the DGLAP evolution by including gluon fusion terms and see that the effect is small at present energies, and, in any case, a strong gluon shadowing is not favored. The region studied ($x \sim 0.01$) is the most relevant for RHIC multiplicities.Comment: 4 pages, 3 postscript figures. Contributed to 37th Rencontres de Moriond on QCD and Hadronic Interactions, Les Arcs, France, 16-23 Mar 200

Global DGLAP fit analyses of the nPDF: EKS98 and HKM

The DGLAP analyses of the nuclear parton distribution functions (nPDF) based on the global fits to the data are reviewed, and the results from EKS98 and HKM are compared. The usefulness of measuring hard probes in $pA$ collisions, at the LHC in particular, is demonstrated.Comment: 10 pages, 3 figures. Contribution to CERN Yellow Report on Hard Probes in Heavy Ion Collisions at the LH

Nuclear size and rapidity dependence of the saturation scale from QCD evolution and experimental data

The solutions of the Balitsky-Kovchegov evolution equations are studied numerically and compared with known analytical estimations. The rapidity and nuclear size dependences of the saturation scale are obtained for the cases of fixed and running coupling constant. These same dependences are studied in experimental data, on lepton-nucleus, deuteron-nucleus and nucleus-nucleus collisions, through geometric scaling and compared with the theoretical calculations.Comment: 8 pages, 8 figures. Contribution based on talks given by J. G. Milhano and C. A. Salgado to the proceedings of ``Hard Probes 2004'', Ericeira (Portugal), November 4-10, 200