Measurement of the ratios of deep inelastic muon-nucleus cross sections on various nuclei compared to deuterium

Results are presented on the ratios of the deep inelastic muon-nucleus cross sections for carbon, copper and tin nuclei to those measured on deuterium. The data confirm that the structure functions of the nucleon measured in nuclei are different from those measured on quasi-free nucleons in deuterium. The kinematic range of the data is such that 〈Q²〉 ∼ 5 GeV² at x ∼ 0.03, increasing to 〈Q²〉 ∼ 35 GeV² for x ∼ 0.65. The measured cross section ratios are less than unity for x ≲ 0.05 and for 0.25 ≲ x < 0.7. The decrease of the ratio below unity for low x becomes larger as A increases as might be expected from nuclear shadowing. However, this occurs at relatively large values of Q² (∼ 5 GeV²) indicating that such shadowing is of patrionic origin.     

The EMC effect — status and perspectives

Recent experimental results on the EMC effect are presented. The ratios of structure functions for nuclei and deuterium measured by the two muon experiments at CERN show a clear enhancement of a few percent forx<0.25. Atx below 0.05 substantial shadowing with littleQ ² dependence has been observed by a dedicated low angle experiment of the EMC. No significant nuclear mass dependence ofR=αL/αT has been seen in the SLAC experiment E 140. There are several indications that theQ ² evolution of nuclear structure functions deviates from the expectations of perturbative QCD and that the gluon distribution in nuclei is harder than in free nucleons. This is possibly caused by nucleon-nucleon correlations on the quark-gluon level. Many aspects of the EMC effect are presently being investigated by the high energy muon experiment of the NMC collaboration at CERN and a Drell-Yan experiment at FNAL. First results can be expected soon. They will help to develop a better understanding of nuclear effects in quark and gluon distributions.     

On the Q 2 dependence of nuclear structure functions

The recent high statistics NMC data on the Tin to Carbon structure function ratio seems to indicate, for the first time, a significant Q ² dependence, especially at small values of Bjorken x, x < 0.05, and Q ² > 1 GeV². A purely log(Q ²)-type dependence of the structure functions, which is consistent with the free nucleon data, yields a fairly flat ratio with little or no Q ² dependence. In view of this seeming contradiction, we re-examine the applicability of such a model to nuclear structure functions in such a kinematical regime. We find that the model is consistent with all data, within experimental errors, without any need for introducing additional Q ² dependences or higher twist contributions. The model correctly reproduces the Q ² dependence of the Carbon structure function as well. We also critically examine the Q ² dependence of the corresponding spin dependent structure functions.     

Inelastic electron scattering from protons and deuterons at very low Q2

The total cross-section for production of hadrons by inelastic electron scattering at 3.2° from hydrogen and deuterium has been measured in the Q² range 0.015 GeV² to 0.1 GeV², at virtual photon energies ranging from 2 GeV to 8.5 GeV. The transition to photoproduction is observed to be smooth, the ratio σ_D/σ_H being about 1.85 in this range. No evidence is seen for a conjectured rapid Q²-dependence of this ratio at low Q².     

Deep inelastic neutrino interactions in the bubble chamber skat at 2–30 GeV

Data on inclusive deep inelastic neutrino interactions at 2–30 GeV are presented. Distributions in x, y and 〈Q²〉 dependence on neutrino energy are compared with quark-parton model predictions. The 〈Q²〉 dependence on energy has the form: 〈Q²〉 = (0.2 ± 0.1) + (0.25 ± 0.02) E_v.     

Phenomenology of nuclear shadowing in deep-inelastic scattering

We investigate shadowing effects in deep-inelastic scattering from nuclei at small valuesx < 0.1 of the Bjorken variable. Unifying aspects of generalized vector meson dominance and color transparency we first develop a model for deep-inelastic scattering from free nucleons at smallx. In application to nuclear targets we find that the coherent interaction of quark-antiquark fluctuations with nucleons in a nucleus leads to the observed shadowing atx < 0.1. We compare our results with most of the recent data for a large variety of nuclei and examine in particular the Q² dependence of the shadowing effect. While the coherent interaction of low mass vector mesons causes a major part of the shadowing observed in the Q² range of current experiments, the coherent scattering of continuum quark-antiquark pairs is also important and guarantees a very weak overall Q² dependence of the effect. We also discuss shadowing in deuterium and its implications for the quark flavor structure of nucleons. Finally we comment on shadowing effects in high-energy photon-nucleus reactions with real photons.     

Semi-inclusive deep inelastic scattering at small-x

We study the semi-inclusive hadron production in deep inelastic scattering at small-x. A transverse-momentum-dependent factorization is found consistent with the results calculated in the small-x approaches, such as the color-dipole framework and the color glass condensate, in the appropriate kinematic region at the lowest order. The transverse-momentum-dependent quark distribution can be studied in this process as a probe for the small-x saturation physics. Especially, the ratio of quark distributions as a function of transverse momentum at different x   demonstrates strong dependence on the saturation scale. The Q²$Q^2$ dependence of the same ratio is also studied by applying the Collins–Soper–Sterman resummation method.     

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.     

A model for FL and R = FL/FT at low x and low Q2

A model for the longitudinal structure function F_L at low x and low Q² is presented, which includes the kinematical constraint F_L ～ Q⁴ as Q² → 0. It is based on the photon-gluon fusion mechanism suitably extrapolated to the region of low Q². The contribution of quarks having limited transverse momentum is treated phenomenologically assuming that it is described by the soft pomeron exchange mechanism. The ratio R = F_L/(F₂ ? F_L), with the F₂ appropriately extrapolated to the region of low Q², is also discussed.     

Color-conductivity in nuclei and the EMC-effect

We advocate that gluons and quarks of sufficiently short wavelengths are delocalized in nuclei. This hypothesis leads us to structure functions measured in μ-nucleus scattering, which depend at fixedx only on the ratio of the resolving power 1/Q and the radius of the nucleusR _A, whereA denotes the mass number of the nucleus. Thus we suggest that the structure functionF ₂(x, Q ²,A) per nucleon of an isoscalar nucleusA scales essentially as \(F_2 (x,Q^2 ,A) = \tilde F_2 (x,R_A^2 \cdot Q^2 )\) with a universal function \(\tilde F_2\) . The ratio of the so obtained structure functions of iron to deuterium agrees rather well with the one measured recently by the European Muon Collaboration. This observation implies that nuclei are “color-insulators” at lowQ ², but “color conductors” at largeQ ².     

Structure of Na2O·MO·SiO2·CaF2 (M=Mg,Ca) oxyfluoride glasses

(9−x)CaO·xMgO·15Na₂O·60SiO₂·16CaF₂(x=0, 2, 4, 6, and 9) oxyfluoride glasses were prepared. Utilizing the Raman scattering technique together with ²⁹Si and ¹⁹F MAS NMR, the effect of alkaline metal oxides on the Q species of glass was characterized. Raman results show that as magnesia is added at the expense of calcium oxide, the disproportional reaction Q³→Q⁴+Q² (Qⁿ is a SiO₄ tetrahedron with n bridging oxygens) prompted due to the high ionic field strength of magnesia, magnesium oxide entered into the silicate network as tetrahedral MgO₄, and removed other modifying ions for charge compensation. This reaction was confirmed by ²⁹Si MAS NMR. ¹⁹F MAS NMR results show that fluorine exists in the form of mixed calcium sodium fluoride species in all glasses and no Si–F bonds were formed. As CaO is gradually replaced by MgO (x=6, 9), a proportion of the magnesium ions combines with fluorine to form the MgF⁺ species. Meanwhile, some part of Na⁺ ions complex F⁻ in the form of F–Na(6).     

Total cross sections and nucleon structure functions in the gargamelle SPS neutrino/antineutrino experiment

Total neutrino and antineutrino cross sections in the energy range 15 to 150 GeV, and the nucleon structure functions, F₂(x, Q²) and xF₃(x, Q²) in the Q² range 0.5 to 50 (GeV/c)² have been measured using a data sample of 3000 neutrino and 3800 antineutrino events. The structure functions show a weak Q² dependence at different x values.     

The EMC effect at low x in perturbative QCD

The EMC effect is studied in the perturbative QCD hard pomeron approach. In this framework the nuclear structure function can be expressed directly in terms of the proton one. In the limit x → 0 and for a nucleus with a constant density the effect is found to be a function of a single variable which combines its x-, Q- and A-dependence. The EMC ratio of the nuclear to nucleon structure functions goes to zero for x → 0 or/and A ? 1. At large Q ² the effect dies out as ln Q/Q. To describe the present data at 0. 005 < x < 0. 05 an attempt is made to take into account subasymptotic effects by introducing an anomalous dimension falling with x. This leads to a weaker x- and Q-dependence, which almost disappears as x grows and the anomalous dimension becomes small.     

Measurement and QCD analysis of the diffractive deep-inelastic scattering cross section at HERA

A detailed analysis is presented of the diffractive deep-inelastic scattering process ep→eXY, where Y is a proton or a low mass proton excitation carrying a fraction 1-x_IP>0.95 of the incident proton longitudinal momentum and the squared four-momentum transfer at the proton vertex satisfies |t|<1 GeV². Using data taken by the H1 experiment, the cross section is measured for photon virtualities in the range 3.5≤Q²≤1600 GeV², triple differentially in x_IP, Q² and β=x/x_IP, where x is the Bjorken scaling variable. At low x_IP, the data are consistent with a factorisable x_IP dependence, which can be described by the exchange of an effective pomeron trajectory with intercept α_IP(0)=1.118±0.008(exp.)^+0.029 _-0.010(model). Diffractive parton distribution functions and their uncertainties are determined from a next-to-leading order DGLAP QCD analysis of the Q² and β dependences of the cross section. The resulting gluon distribution carries an integrated fraction of around 70% of the exchanged momentum in the Q² range studied. Total and differential cross sections are also measured for the diffractive charged current process e⁺p→ν̄_eXY and are found to be well described by predictions based on the diffractive parton distributions. The ratio of the diffractive to the inclusive neutral current ep cross sections is studied. Over most of the kinematic range, this ratio shows no significant dependence on Q² at fixed x_IP and x or on x at fixed Q² and β.     

Deep-inelastic scattering in κ factorization and the anatomy of the differential gluon structure function of the proton

The differential gluon structure function of the proton, ?(x, Q ²), introduced by Fadin, Kuraev, and Lipatov in 1975 is extensively used in small-x QCD. We report here the first determination of ?(x, Q ²) from experimental data on the small-x proton structure function F _2p (x, Q ²). We give convenient parametrizations for ?(x, Q ²) based partly on the available DGLAP evolution fits (GRV, CTEQ, and MRS) to parton distribution functions and on realistic extrapolations into the soft region. We discuss the impact of soft gluons on various observables. The x dependence of the so-determined ?(x, Q ²) varies strongly with Q ² and does not exhibit simple Regge properties. Nonetheless, the hard-to-soft diffusion is found to give rise to a viable approximation of the proton structure function F _2p (x, Q ²) by the soft and hard Regge components with intercepts Δ_soft=0 and Δ_hard ～ 0.4.     

Origin of the Q 2-dependence of the DIS structure functions

We consider in detail Q ²-dependence of the DIS structure functions. Very often this dependence is claimed to be originated by the Q ²-dependence of the QCD coupling. This leads to the small-x asymptotics of the structure functions with Q ²-dependent intercepts. We demonstrate that the DGLAP parametrization α _s = α _s (Q ²) is an approximation valid in the region of large x (where 2pq can be approximated by Q ²) only, providing the factorization scale is also large. Outside this region, the DGLAP parametrization fails, so α _s should be replaced by an effective coupling which is independent of Q ² at small x. As a consequence, intercepts of the structure functions are independent of Q ² . Nevertheless, the small-x asymptotics of the structure functions explicitly depend on Q ² , even when the coupling does not depend on it. We also consider the structure functions at small Q ² and give a comment on power-Q ² corrections to the structure functions at large and small Q ² .     

Scaling violation in the pion structure function

TheQ ²-dependence of the pion structure function extracted from high transverse momentum π⁰ production cross sections is examined. We find, in thex→1 region, that this dependence can be parametrized by a power of (1?x) increasing as ln lnQ ². This is in agreement with the expectations of asymptotic freedom and also seen in the structure function extracted from dilepton production. It is not possible to fit all of theQ ²-dependence with a simple power law term.     

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.