Experimental results of inclusive hard-process cross sections in heavy-ion collisions conventionally lean on a normalization computed from Glauber models where the inelastic nucleon-nucleon cross section $σ_{\rm nn}^{\rm inel}$ -- a crucial input parameter -- is simply taken from proton-proton measurements. In this letter, using the computed electro-weak boson production cross sections in lead-lead collisions as a benchmark, we determine $σ_{\rm nn}^{\rm inel}$ from the recent ATLAS data. We find a significantly suppressed $σ_{\rm nn}^{\rm inel}$ relative to what is usually assumed, show the consequences for the centrality dependence of the cross sections, and address the phenomenon in an eikonal minijet model with nuclear shadowing.
The inclusive spectra of secondaries produced in soft (minimum-bias) p+Pb collisions at LHC energy are calculated in the frame of the Quark-Gluon String Model, by including the inelastic screening corrections (percolation effects). These effects are expected to be quite large at the very high energies, and they should drive down the spectra in the midrapidity region more than 2 times, at sqrt(sNN)=5 TeV.
Nuclear structure functions at small x and small or moderate $Q^2$ are studied using the relation with diffraction on nucleons which arises from Gribov's Reggeon Calculus. A reasonable description of experimental data is obtained with no fitted parameters. A comparison with other models and predictions for future lepton-ion colliders are provided. Consequences for the reduction of multiplicities in nucleus-nucleus collisions at energies of RHIC and LHC are examined.
Different types of high-energy hadron-nucleus cross sections are discussed emphasizing the role played by Nucleon-Nucleon (NN) Short-Range Correlations (SRC) and Gribov Inelastic Shadowing (IS)
The importance of the effects of nucleon-nucleon (NN) short-range correlations (SRC) and Gribov inelastic shadowing (IS) on various high energy scattering processes involving nuclear targets is demonstrated within an improved Glauber-Gribov approach.
We discuss the close relation between shadowing in deep-inelastic lepton-nucleus scattering and diffractive photo- and leptoproduction of hadrons from free nucleons. We show that the magnitude of nuclear shadowing at small Bjorken-x, as measured by the E665 and NMC collaborations, is directly related to HERA data on the amount of diffraction in the scattering from free nucleons.
The dipole phenomenology, which has been quite successful applied to various hard reactions, especially on nuclear targets, is applied for calculation of Gribov inelastic shadowing. This approach does not include ad hoc procedures, which are unavoidable in calculations done in hadronic representation. Several examples of Gribov corrections evaluated within the dipole description are presented.
We discuss shadowing corrections to the structure function $F_2$ in neutrino deep-inelastic scattering on heavy nuclear targets. In particular, we examine the role played by shadowing in the comparison of the structure functions $F_2$ measured in neutrino and muon deep inelastic scattering. The importance of shadowing corrections in the determination of the strange quark distributions is explained.
We discuss effect of nuclear shadowing in neutrino deep-inelastic scattering in terms of non perturbative parton model. We found that for small Bjorken $x$ and large $Q^2$ the structure function $F_3$ is shadowed in nuclei about two times as stronger as $F_2$. The underlying reason and phenomenological aspects of this observation are discussed.
We investigate the nuclear shadowing mechanism in the context of perturbative QCD and the Glauber multiple scattering model. Using recent HERA data on nucleon structure function at small $x$, we put stringent constrains on the nucleon gluon density in the double-logarithm approximation. We suggest that the scaling violation of the nucleon structure function in the region of small $x$ and semihard scale $Q^2$ can be reliably described by perturbative QCD which is a central key to the understanding of the scale dependence of the nuclear shadowing effect. Our results indicate that while the shado…
Nuclear shadowing corrections to the structure functions of deep inelastic scattering of intermediate-mass nuclei are calculated at very low values of Bjorken x and small values of Q^2 (Q^2<5 GeV^2). The two-component approach (generalized VMD plus hard pomeron) is used for a description of the underlying virtual photon - nucleon interaction. The hard component of the nucleon structure function is calculated in a framework of the colour dipole model with dipole cross section having Regge-type energy dependence. Numerical results for nuclear shadowing corrections are compared with available dat…
Shadowing effects in deep-inelastic lepton-nucleus scattering probe the mass spectrum of diffractive leptoproduction from individual nucleons. We explore this relationship using current experimental information on both processes. In recent data from the NMC and E665 collaboration, taken at small x << 0.1 and Q^2 < 1 GeV^2, shadowing is dominated by the diffractive excitation and coherent interaction of low mass vector mesons. If shadowing is explored at small x << 0.1 but large Q^2 >> 1 GeV^2 as discussed at HERA, the situation is different. Here dominant contributions come from the coherent i…
The coherence of multiscattering quark nuclear processes leads to shadowing and antishadowing of the electromagnetic nuclear structure functions in agreement with measurements. This picture leads to substantially different antishadowing for charged and neutral current processes, particularly in anti-neutrino reactions, thus affecting the extraction of the weak-mixing angle $\sin^2θ_W$.
The measurement of the nuclear structure function $F_2^A (x,Q^2)$ at the future electron-ion collider (EIC) will be of great relevance to understand the origin of the nuclear shadowing and to probe gluon saturation effects. Currently there are several phenomenological models, based on very distinct approaches, which describe the scarce experimental data quite successfully. One of main uncertainties comes from the schemes used to include the effects associated to the multiple scatterings and to unitarize the cross section. In this paper we compare the predictions of three different unitarizatio…
The Glauber modeling plays a key role in centrality-dependent measurements of heavy-ion collisions. A central input parameter in Glauber models is the inelastic nucleon-nucleon cross section $σ_{\text{nn}}^{\text{inel}}$ which is nearly always taken from proton-proton measurements. At the LHC energies $σ_{\text{nn}}^{\text{inel}}$ depends on the QCD dynamics at small $x$ and low interaction scales where the shadowing/saturation phenomena are expected to become relatively more important for larger nuclei than for the proton. Thus, $σ_{\text{nn}}^{\text{inel}}$ e.g. in Pb+Pb collisions may well …
We use several diverse parameterizations of diffractive parton distributions, extracted in leading twist QCD analyses of the HERA diffractive deep inelastic scattering (DIS) data, to make predictions for leading twist nuclear shadowing of nuclear quark and gluon distributions in DIS on nuclei. We find that the HERA diffractive data are sufficiently precise to allow us to predict large nuclear shadowing for gluons and quarks, unambiguously. We performed detailed studies of nuclear shadowing for up and charm sea quarks and gluons within several scenarios of shadowing and diffractive slopes, as w…
A model for shadowing in nuclear structure functions at small $x$ and small or moderate $Q^2$ is presented using the relation with diffraction that arises from Gribov's reggeon calculus. A reasonable description of the experimental data is obtained with no fitted parameters. A comparison with predictions from other models is performed.
Nuclear shadowing corrections to the structure functions of deep inelastic scattering on intermediate-mass nuclei are calculated at very small values of Bjorken x and small values of Q^2 (Q^2<5 Gev^2). The two-component approach developed in previous works of authors for a description of the nucleon structure functions of deep inelastic scattering is used. It is shown that the hard component of the nucleon structure functions that arises, in terms of the colour dipole model, from qq-pairs with a high transverse momentum, is almost not shadowed. It is shown that a change of the slope of the sha…
We discuss the experimental indications on the behaviour of F_2(x,Q^2) at small x both in proton and nuclear targets. By comparing the parametrizations of the data we conclude that shadowing correction effects in a proton target can appear at a noticeable level for x=(2 - 4)\times10^{-4} and Q^2\sim 10^1 GeV^2, namely inside the HERA regime.
The centrality dependence of pseudorapidity density of charged particles ($ dN_{ch}/dη$) in $Cu+Cu$ ($Au+Au$) collisions at RHIC energy of $ \sqrt{s_{_{\rm NN}}}=22.4$ , $62.4 $ and $200$ ($19.6$, $62.4$ and $200$) GeV, is investigated within an improved HIJING code. The standard HIJING model is enhanced by a prescription for collective nucleon-nucleon ($NN$) interactions and more modern parton distribution functions. The collective $NN$-interactions are used to induce both cascade and nucleon shadowing effects. We find collective cascade broadens the pseudorapidity distributions in the tails …
This review outlines our present experimental knowledge and theoretical understanding of deep-inelastic scattering on nuclear targets. The emphasis is primarily on nuclear coherence phenomena, such as shadowing, where the key physics issue is the exploration of hadronic and quark-gluon fluctuations of a high-energy virtual photon and their passage through the nuclear medium. New developments in polarized deep-inelastic scattering on nuclei are also discussed, and more conventional binding and Fermi motion effects are summarized. The report closes with a brief outlook on vector meson electropro…
In the framework of the collinear factorized pQCD approach we calculate the small-$x_B$ process-dependent nuclear modification to the structure functions measured in neutrino-nucleus deeply inelastic scattering. We include both heavy quark mass corrections $(M^2/Q^2)$ and resummed nuclear-enhanced dynamical power corrections in the quantity $(ξ^2/Q^2)(A^{1/3}-1)$ with $ξ^2$ evaluated to leading order in $α_s$. Our formalism predicts a measurable difference in the shadowing pattern of the structure functions $F_2^A(x_B,Q^2)$ and $F_3^A(x_B,Q^2)$ and a significant low- and moderate-$Q^2$ modific…
While the phenomenon of gluon nuclear shadowing at small $x$ has been getting confirmation in QCD analyses of various LHC measurements involving heavy nuclei, it has not been possible so far to establish experimentally the number of target nucleons responsible for nuclear shadowing in a given process. To address this issue, we study coherent $J / ψ$ electroproduction on $^4$He and $^3$He in the kinematics of a future electron-ion collider and show that this process has the power to disentangle the contributions of the interaction with a specific number of nucleons $k$, in particular, with two …
Shadowing is a quantum phenomenon leading to a non-additivity of electroweak cross sections on nucleons bound in a nucleus. It occurs due to destructive interference of amplitudes on different nucleons. Although the current experimental evidence for shadowing is dominated by charged-lepton nucleus scattering, studies of neutrino nucleus scattering have recently begun and revealed unexpected results.
We calculate shadowing in the process of deep inelastic interactions of leptons with nuclei in the perturbative regime of QCD. We find appreciable shadowing for heavy nuclei (e.g. Pb) in the region of small Bjorken scaling variable $10^{-5}\leq x \leq 10^{-3}$. This shadowing depends weakly on $Q^2$, but it may be strongly influenced, especially at $x \geq 10^{-3}$, by the existence of real parts of the forward scattering amplitudes.
The strange sea quarks distributions of nucleons obtained by two global analyses based on available structure function data of muon and neutrino deep inelastic scatterings are different from the strange sea quark distribution measured by the CCFR Collaboration from dimuon events in neutrino scattering. We discuss possible contributions to this discrepancy from the nuclear shadowing in the deuteron and from the isospin symmetry breaking in the sea between the neutron and the proton.
A model for the description of photonuclear reactions in the multi-GeV range is described that combines the coherent initial state interactions (shadowing) of the incoming photon with an incoherent coupled channel description of final state interactons of outgoing particles. Particle production itself is treated either, at low energies, through nucleon resonance decays or, at higher energies, through string fragmentation. The initial state nucleons can be far-off-shell due to ground state correlations. Results are shown for semi-inclusive meson production.
We extend the theory of leading twist nuclear shadowing to calculate leading twist nuclear diffractive parton distribution functions (nDPDFs). We observe that the quark and gluon nPDFs have different patterns of the $A$-dependence. It is found that the probability of diffraction in the quark channel increases with $A$, reaching about 30% at $x \sim 10^{-4}$ for $A \sim 200$, and weakly decreases with $Q^2$. In the gluon channel, the probability of diffraction is large for all nuclei ($\sim 40$% for heavy nuclei at $x \sim 10^{-4}$ and $Q_0^2 \sim 4$ GeV$^2$), it weakly depends on $A$ and it de…
We study medium modifications of J/psi production in cold nuclear media in deuterium-nucleus collisions. We discuss several parameterizations of the modifications of the parton densities in the nucleus, known as shadowing, an initial-state effect. We also include absorption of the produced J/psi by nucleons, a final-state effect. Both spatially homogeneous and inhomogeneous shadowing and absorption are considered. We use the number of binary nucleon-nucleon collisions as a centrality measure. Results are presented for d+Au collisions at sqrt{S_{NN}} = 200 GeV and for d+Pb collisions at sqrt{S_…
We explore how nuclear modifications to the nucleon structure functions, shadowing, affect massive gauge boson production in heavy ion collisions at different impact parameters. We calculate the dependence of $Z^0$, $W^+$ and $W^-$ production on rapidity and impact parameter to next-to-leading order in Pb+Pb collisions at 5.5 TeV/nucleon to study quark shadowing at high $Q^2$. We also compare our Pb+Pb results to the $pp$ rapidity distributions at 14 TeV.
We explore how nuclear modifications to the nucleon parton distributions affect production of high-$p_T$ hadrons in heavy ion collisions. We perform a leading order calculation of the high-$p_T$ charged pion, kaon and proton spectra using standard fragmentation functions and shadowing parameterizations. We also consider alternate models of shadowing. Near midrapidity, shadowing is a small effect and cannot explain the large observed suppression of high-$p_T$ hadrons. We also consider the isospin difference between protons and nuclei and find that it is also a small effect on high-$p_T$ hadron …
We consider the behavior of the slope of the nuclear structure function $F_2^A$ in the kinematic region which will be explored in the eA HERA collider. We demonstrate that, similarly to the nucleon case, a `turn over' is predicted in this observable. Moreover, we predict that the presence of the shadowing corrections implies that the maximum value of the slope is dependent of the number of nucleons A, differently from the DGLAP predictions. Our conclusion is that the measurement of this observable will allow to evidentiate the presence of the shadowing corrections.
In this paper, the implication of the extreme large $N_c$ limit for nucleon-nucleon cross section is examined. Starting from the $N_c$ scaling of the S-matrix elements, a relation between the total inelastic and total cross sections is derived for the regime in which the momenta are much larger than the QCD scale. A conceptual complication arise from the fact that there is a tower of baryons, such as the $Δ$, with mass splittings from the nucleon which go to zero at large $N_c$. Since these baryons are stable at large $N_c$, the meaning of elasticity must be modified. Processes which only tran…
A process of inelastic nucleon-nucleon collisions with the impact parameter less than a radius of the nucleon quark core is considered. The criteria for selection of such collisions from a full array of the nucleon-nucleon interactions are suggested.
The current normalization of the cross section of inclusive high-pT particle production in deuteron-gold collisions measured RHIC relies on Glauber calculations for the inelastic d-Au cross section. These calculations should be corrected for diffraction. Moreover, they miss the Gribov's inelastic shadowing which makes nuclei more transparent (color transparency). The magnitude of this effect rises with energy and it may dramatically affect the normalization of the RHIC data. We evaluate these corrections employing the light-cone dipole formalism and found a rather modest corrections for the cu…
Relying on previous results that link entanglement entropy and parton distribution functions in deep inelastic scattering and focusing on the small Bjorken scaling region we present here indications that gluon shadowing might indeed be explained as due to a depletion of the entanglement entropy between observed and unobserved degrees of freedom per nucleon within a nucleus with respect to the free nucleon case. We apply to gluon shadowing the general Page approach to the calculation of the entanglement entropy in bipartite systems, giving physical motivations of the results.
The proton structure function is re-deduced from the data of deep inelastic electron-proton scattering after enhanced correction that is made due to the multiple scattering effect. The Glauber approach is used to account for the multiple scattering of electron with the quark constituents of the proton. The results are compared with the prediction of the parton model. Appreciable deviation is observed only at low values of the Bjorken scaling, which correspond to the extremely deep inelastic scattering.
We argue that with an increase of the collision energy, elastic photoproduction of $ρ$ mesons on nuclei becomes affected by the significant cross section of photon inelastic diffraction into large masses, which results in the sizable inelastic nuclear shadowing correction to $σ_{γA \to ρA}$ and the reduced effective $ρ$-nucleon cross section. We take these effects into account by combining the vector meson dominance model, which we upgrade to include the contribution of high-mass fluctuations of the photon according to QCD constraints, and the Gribov-Glauber approximation for nuclear shadowing…
A hybrid model is used to describe the energy loss of very high-energy taus and muons in matter due to inelastic scattering on nuclei. The model involves soft and semihard photonuclear interactions as well as the deep inelastic scattering including the weak neutral current processes. For the lepton scattering on nuclei all important nuclear effects, the shadowing, anti-shadowing, EMC and the nucleon binding, were taken into account. Approximating formulas for the muon and tau energy loss portion by the inelastic scattering on nuclei in water are given for wide energy range up to $10^9$ GeV.
We present a new analysis of the E772 and E866 experiments on the nuclear dependence of Drell-Yan (DY) lepton pair production resulting from the bombardment of $^2H$, Be, C, Ca, Fe, and W targets by 800 GeV/c protons at Fermilab. We employ a light-cone formulation of the DY reaction in the rest frame of the nucleus, where the dimuons detected at small values of Bjorken x_2 << 1 may be considered to originate from the decay of a heavy photon radiated from an incident quark in a bremsstrahlung process. We infer the energy loss of the quark by examining the suppression of the nuclear-dependent DY…
The shadowing and antishadowing of nuclear structure functions in the Gribov-Glauber picture is due respectively to the destructive and constructive interference of amplitudes arising from the multiple-scattering of quarks in the nucleus. The effective quark-nucleon scattering amplitude includes Pomeron and Odderon contributions from multi-gluon exchange as well as Reggeon quark-exchange contributions. We show that the coherence of these multiscattering nuclear processes leads to shadowing and antishadowing of the electromagnetic nuclear structure functions in agreement with measurements. This…
We consider deep-inelastic lepton scattering, Drell-Yan lepton pair and heavy quark production in the reference frame of the target. These reactions traditionally treated as hard have, however, a substantial leading twist soft contribution. One of the manifestations of such a soft component, nuclear shadowing, is overviewed.
The Bloom-Gilman local duality of the inelastic structure function of the proton, the deuteron and light complex nuclei is investigated using available experimental data in the squared four-momentum transfer range from 0.3 to 5 (GeV/c)**2. The results of our analysis suggest that the onset of the Bloom-Gilman local duality is anticipated in complex nuclei with respect to the case of the protonand the deuteron. A possible interpretation of this result in terms of a rescaling effect is discussed with particular emphasis to the possibility of reproducing the damping of the nucleon-resonance trans…
We consider the effect of nuclear shadowing in polarized deep inelastic scattering (DIS) on ^6LiD at small Bjorken x and its relevance to the extraction of the deuteron spin structure function g_{1}^{d}(x,Q^2). Using models, which describe nuclear shadowing in unpolarized DIS, we demonstrate that the nuclear shadowing correction to g_{1}^{d}(x,Q^2) is significant.
Based on the requirement in the simulation of lepton-nucleus deep inelastic scattering (DIS), we construct a fortran program LDCS 1.0 calculating the differential and total cross sections for the unpolarized charged lepton-unpolarized nucleon and neutrino-unpolarized nucleon neutral current (charged current) DIS at leading order. Any set of the experimentally fitted parton distribution functions could be employed directly. The mass of incident and scattered leptons is taken into account and the boundary conditions calculating the single differential and total cross section are studied. The cal…
A covariant formulation of spin-dependent deep-inelastic scattering from nuclei is presented. In the relativistic impulse approximation the inclusive nuclear cross section is described in terms of the amplitude for forward, virtual-photon scattering from an off-mass-shell nucleon. The general structure of the off-shell nucleon hadronic tensor is derived, and the leading behavior of the off-shell nucleon structure functions computed in the Bjorken limit. The formalism, which is valid for nucleons bound inside nuclei with spin 1/2 or 1, is applied to the case of the deuteron.
The relation between diffraction in lepton-proton collisions and shadowing of nuclear structure functions which arises from Gribov inelastic shadowing, is described. A model realizing such relation, which produces a parameter-free description of experimental data on nuclear structure functions at small $x$, is presented. The application to the description of multiplicities in nuclear collisions is discussed and related to other approaches.
New data from HERA experiment on deep inelastic scattering have been used to parametrize nucleon and Pomeron structure functions. Within the Gribov theory, the parameterizations were employed to calculate gluon shadowing for various heavy ions. The latter was compared with predictions from other models. Calculations of multiplicity reduction due to gluon shadowing for d+Au collisions at forward rapidities at $\sqrt{s}$=200 GeV are in good agreement with BRAHMS data on the nuclear modification factor.
