Structure functions of bound nucleons: From the EMC effect to nuclear shadowing

We describe the nuclear structure functions in the whole range of the Bjorken variablex, by combining various effects in a many-step procedure. First, we present a QCD motivated model of nucleons, treated, in the limit of vanishingQ ², as bound states of three relativistic constituent quarks. Gluons and sea quarks are generated radiatively from the input valence quarks. All parton distributions are described in terms of the confinement (or nucleon's) radius. The results for free nucleons are in agreement with the experimental determinations. The structure functions of bound nucleons are calculated by assuming that the main effect of nucleon binding is stretching of nucleons. The larger size of bound nucleons lowers the valence momentum and enhances the radiatively generated glue and sea densities. In the small-x region the competitive mechanism of nuclear shadowing takes place. It also depends on the size of the nucleons. By combining stretching, shadowing and Fermi motion effects (the latter confined to very largex), the structure function ratio is well reproduced. Results are also presented for theA-dependence of the momentum integral of charged partons, the nuclear gluon distribution and the hadron-nuclei cross sections.     

Shadowing effects in nuclear parton distributions for small values ofx

The shadowing corrections to gluon and quark distributions in nuclei in the region of small values ofx are discussed. They are related to parton distributions in a pomeron which are in principle measurable in hard diffractive processes on the nucleon target. Multiple scattering corrections to shadowing are considered in a model dependent way. The perturbative QCD evolution of shadowing is also taken into account. Various possibilities of the partonic content of a pomeron are considered. It is shown in particular that the conventional parametrizations of parton distributions in a pomeron which are based on the assumption that it consists mostly of gluons imply substantial nuclear shadowing in gluon distributions in heavy nuclei. Possible phenomenological implications of shadowing corrections in nuclear parton distributions for various semi-hard processes with nuclear targets are briefly discussed.     

Implication of the overlap representation for modelling generalized parton distributions

Based on a field theoretically inspired model of light-cone wave functions, we derive valence-like generalized parton distributions and their double distributions from the wave function overlap in the parton number conserved s-channel. The parton number changing contributions in the t-channel are restored from duality. In our construction constraints of positivity and polynomiality are simultaneously satisfied and it also implies a model dependent relation between generalized parton distributions and transverse momentum dependent parton distribution functions. The model predicts that the t  -behavior of resulting hadronic amplitudes depends on the Bjorken variable xBj$x_{\mathrm{Bj}}$. We also propose an improved ansatz for double distributions that embeds this property.     

DVCS on nuclei: observability and consequences

In this paper, we discuss the feasibility of measuring deeply virtual Compton scattering (DVCS) on nuclei in a collider setting, as for example, the planned high-luminosity Electron-Ion Collider (EIC). We demonstrate that employing our recent model for nuclear generalized parton distributions (nGPDs), the one-photon unpolarized DVCS cross section as well as the azimuthal and spin asymmetry are of the same size as in the proton case. This will allow for an experimental extraction of nuclear GPDs with high precision, shedding new light not only on nuclear shadowing at small x_Bj but also on the interplay of shadowing and nuclear enhancement at .Received: 8 September 2003, Revised: 24 November 2003, Published online: 15 January 2004     

Chiral Expansion of Nucleon PDF at x ~ m π /M N

Based on the chiral perturbation theory, we investigate the low-energy dynamics of nucleon parton distributions. We show that in different regions of the momentum fraction x the chiral expansion is significantly different. For nucleon parton distributions these regions are characterized by x ~ 1, x ~ m _π /M _N and \({x \sim (m_{\pi}/M_{N})^2}\) . We derive extended counting rules for each region and obtain model-independent results for the nucleon parton distributions down to \({x \gtrsim m^{2}_{\pi}/M^2_{N} \approx 10^{-2} }\) .     

Hadron production in 200 GeV μ-copper and μ-carbon deep inelastic interactions

The measurements of the z and p_T² distribution of hadrons produced in the interactions of 200 GeV muons with copper and carbon nuclei are shown in different x_Bj and virtual photon energy intervals. Effects of the jet scattering are seen at the lowest virtual photon energies while for energies above 70 GeV there is no evidence of these effects. Comparison with a theoretical model indicates that at high jet energies the parton fragmentation distance is greater than the nuclear radius and that the parton absorption cross section is less than 10 mb.     

Shadowing in deep inelastic muon scattering from nuclear targets

Results are presented on the ratio of the inelastic muon-nucleus cross section per nucleon for carbon and calcium relative to that for deuterium. The measurements were made in the kinematic range of low x (0.003–0.1) and low Q² (0.3–3.2 GeV²) at an incident muon energy of 280 GeV. The calcium to deuterium ratio shows a significant x dependence which is interpreted as a shadowing effect. No strong Q² dependence is observed. This suggests that the effect is due at least partially to parton interactions within the nucleus.     

Effect of parton shadowing on the distributions of global observables

The effect of parton shadowing on the distributions of global observables (total transverse energy E _T and charged-particle multiplicity n _ch) is investigated on the basis of the HIJING model of nucleus-nucleus interactions. It is shown that, for the interaction of lead nuclei at $\sqrt s = 5$ TeV per nucleon, the shadowing effect results in a considerable reduction of the cross section for (mini)jet production (approximately by a factor of 4); this in turn reduces the total transverse energy and the charged-particle multiplicity by a factor of 2.7. Upon taking into account the QCD evolution of nuclear structure functions in Q ², the shadowing effect becomes less pronounced (by a factor of 1.9 for PbPb interactions). It is shown that global observables can be used to test models of parton shadowing.     

Testing the scale dependence of the scale factor σ eff in double dijet production at the LHC

The scale factor σ _eff is the effective cross section used to characterize the measured rate of inclusive double dijet production in high-energy hadron collisions. It is sensitive to the two-parton distributions in the hadronic projectile. In principle, the scale factor depends on the center of mass energy and on the minimal transverse energy E _T,min? of the jets contributing to the double dijet cross section. Here, we point out that proton–proton collisions at the LHC will provide for the first time experimental access to these scale dependences in a logarithmically wide, nominally perturbative kinematic range 10?E _T,min??100 GeV. This constrains the dependence of two-parton distribution functions on parton momentum fractions and parton localization in impact parameter space. Novel information is to be expected about the transverse growth of hadronic distribution functions in the range of semi-hard Bjorken x (0.001?x?0.1) and high resolution Q ². We discuss to what extent one can disentangle different pictures of the x-evolution of two-parton distributions in the transverse plane by measuring double-hard scattering events at the LHC.     

Roles of survival probability and barrier reduction in heavy ion fusion induced by break up

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 interaction of diffractively produced heavy mass states. Furthermore we observe that the energy dependence of shadowing is directly related to the mass dependence of the diffractive production cross section for free nucleon targets.     

What can Drell-Yan data tell us about the EMC effect and nucleon parton distributions?

We show that knowledge of thex ₁ andx ₂ dependence of the ratio of Drell-Yan cross-sections measured on heavy nuclei and deuterium can give us information about the origin of the EMC effect. Conversely, we show that an understanding of the EMC effect, together with (non-ratio) Drell-Yan data, can provide us with a way of discriminating between candidates for nucleon parton distributions.     

The physical structure of non-scaling parton models

We discuss the nature of the constituent system seen by probe of momentum Q in non-scaling parton models. The dependence at fixed energy of the parton transverse momentum upon x, the longitudinal momentum fraction, is also investigated. On rather general grounds it is shown that it will increase with x at large x and in a particular model it is found to decrease with x at small x.     

A possible determination of the quark radiation length in cold nuclear matter

We calculate the differential Drell-Yan production cross section in proton-nucleus collisions by including both next-to-leading order perturbative effects and effects of the nuclear medium. We demonstrate that dilepton production in fixed target experiments is an excellent tool to study initial-state parton energy loss in large nuclei and to accurately determine the stopping power of cold nuclear matter. We provide theoretical predictions for the attenuation of the Drell-Yan cross section at large values of Feynman xF and show that for low proton beam energies experimental measurements at Fermilab?s E906 can clearly distinguish between nuclear shadowing and energy loss effects. If confirmed by data, our results may help determine the quark radiation length in cold nuclear matter X₀∼¹⁰−13 m.     

Spin structure of the nucleon—status and recent results

After the initial discovery of the so-called “spin crisis in the parton model” in the 1980s, a large set of polarization data in deep inelastic lepton-nucleon scattering was collected at labs like SLAC, DESY and CERN. More recently, new high precision data at large x and in the resonance region have come from experiments at Jefferson Lab. These data, in combination with the earlier ones, allow us to study in detail the polarized parton densities, the Q² dependence of various moments of spin structure functions, the duality between deep inelastic and resonance data, and the nucleon structure in the valence quark region. Together with complementary data from HERMES, RHIC and COMPASS, we can put new limits on the flavor decomposition and the gluon contribution to the nucleon spin. In this report, we provide an overview of our present knowledge of the nucleon spin structure and give an outlook on future experiments. We focus in particular on the spin structure functions g₁ and g₂ of the nucleon and their moments.     

Parton densities beyond perturbation theory

I compute non-perturbative corrections to the kernel governing the evolution of non-singlet parton densities. The model used is QED in the limit of many charged particles. I find an infrared renormalon at b₀t = −1, where t is the Borel variable and b₀ is the first coefficient of the β-function. This term has a non-trivial dependence on the variable x = -q²/(2p · q) and its coefficient scales as x³/(1 − x)² (p is the momentum of the hadron and q is the momentum transfer). An extrapolation of my results to QCD implies a breakdown of the parton model near the elastic region.     

Quarkonium plus prompt-photon associated hadroproduction and nuclear shadowing

Quarkonium hadroproduction in association with a photon at high energies provides a probe of the dynamics of the strong interactions as it is dependent on the nuclear gluon distribution. Therefore, it could be used to constrain the behavior of the nuclear gluon distribution in proton–nucleus and nucleus–nucleus collisions. Such processes are useful to single out the magnitude of the shadowing/antishadowing effects in the nuclear parton densities. In this work we investigate the influence of nuclear effects in the production of J/ψ+γ and ?+γ and estimate the transverse momentum dependence of the nuclear modification factors. The theoretical framework considered in the J/ψ (?) production associated with a direct photon at the hadron collider is the non-relativistic QCD (NRQCD) factorization formalism.     

Nuclear effects on J/ψ production in proton–nucleus collisions

The study of nuclear effects for J/ψ production in proton–nucleus collisions is crucial for a correct interpretation of the J/ψ suppression patterns experimentally observed in heavy-ion collisions. By means of three representative sets of nuclear parton distribution, the energy loss effect in the initial state and the nuclear absorption effect in the final state are taken into account in the uniform framework of the Glauber model. A leading order phenomenological analysis is performed on J/ψ production cross-section ratios R _W/Be (x _F) for the E866 experimental data. The J/ψ suppression is investigated quantitatively due to the different nuclear effects. It is shown that the energy loss effect with resulting in the suppression on R _W/Be (x _F) is more important than the nuclear effects on parton distributions in high x _F region. The E866 data in the small x _F keep out the nuclear gluon distribution with a large anti-shadowing effect. However, the new HERA-B measurement is not in support of the anti-shadowing effect in the nuclear gluon distribution. It is found that the J/ψ–nucleon inelastic cross section $\sigma^{J/\psi}_{\mathrm{abs}}$ depends on the kinematical variable x _F, and increases as x _F in the region x _F>0.2.     

A search for the S(1936) in 100 GeV pBe interactions

A search for the S(1936) has been made in the invariant mass spectrum of p?p-pairs produced inclusively in proton-beryllium interactions at 100 GeV incident momentum. No enhancement is observed, giving a 3 standard deviation upper limit on the cross section of 220 nb/nucleon for production of a narrow p?p state around ≈ 1940 MeV in the x_F range 0.18 <x_F<0.48.     

Scaling and non-scaling in a rest frame quark-parton model of the proton

Electron-proton deep inelastic scattering is treated as the incoherent scattering of electrons by bound Dirac partons in the proton rest frame. An approximate bound state wave function is used for the initial parton, while the final parton is considered free. A good fit is obtained to the structure function F₁(x,Q²) in the range x > 0.15, Q² > 2 GeV. The subsequent prediction for F₂(x,Q²) is not as good, indicating a small additional contribution by longitudinal photons for W < 2.5 GeV. The parton momentum distribution is found to contain transverse momentum of 400–600 MeV, increasing with x.