Functions of the nucleon structure and determination of the strong coupling constant

The properties of deep inelastic scattering at high energies, as well as results of fitting of experimental data on structure functions, obtained by BCDMS, SLAC, NMC, and BFP collaborations in fixed target experiments, with the aim of determining the strong coupling constant, the shape of parton distributions, and power corrections to F ₂(x, Q ²), are presented.     

Nuclear effects in deep inelastic scattering of charged-current neutrino off nuclear target

The nuclear effects in the neutrino–nucleus charged-current inelastic scattering process is studied by analyzing the CCFR and NuTeV data. The structure functions F₂(x,Q²) and xF₃(x,Q²) as well as differential cross sections are calculated by using CTEQ parton distribution functions and the EKRS and HKN nuclear parton distribution functions, and these are compared with the CCFR and NuTeV data. It is found that the corrections of the nuclear effect to the differential cross section for the charged-current antineutrino scattering on the nucleus are negligible, the EMC effect exists in the neutrino structure function F₂(x,Q²) in the large x region, the shadowing and anti-shadowing effect occur in the distribution functions of valence quarks in the small and medium x region, respectively. It is also found that shadowing effects on F₂(x,Q²) in the small x region in the neutrino–nucleus and the charged-lepton–nucleus deep inelastic scattering processes are different. It is clear that the neutrino–nucleus deep inelastic scattering data should further be employed in restricting the nuclear parton distributions. PACS 13.15.+g; 24.85.+p; 25.30.-c     

Implications of new deep inelastic scattering data for parton distributions

We perform a next-to-leading order structure function analysis of μN and νN deep inelastic data in an attempt to resolve the disagreement between recent EMC and BCDMS measurements of F₂ for μp scattering. Equally acceptable QCD fits are obtained including either set of μN data, but a comparison with Drell-Yan data appears to favour the parton distributions derived from the BCDMS data.     

Analytic and “frozen” coupling constants in QCD up to NNLO from DIS data

Deep inelastic scattering data on the F ₂ structure function provided by the BCDMS, SLAC, and NMC Collaborations are analyzed in the nonsinglet approximation with the analytic and “frozen” modifications of the strong-coupling constant featuring no unphysical singularity (the Landau pole). Improvement of agreement between theory and experiment, with respect to the case of the standard perturbative definition of α _s considered recently, is observed and the higher-twist terms are shown to reduce at the next-to-next-to-leading order accuracy thus confirming earlier studies.     

The effect of quark exchange in A = 3 mirror nuclei and neutron/proton structure functions ratio

By using the quark-exchange formalism, the realistic Faddeev wave function and the Fermi motion effect, we investigate the deep inelastic electron scattering from A = 3 mirror nuclei in the deep-valence region. The initial valence quark input is taken from the GRV's (Glück, Reya and Vogt) fitting procedure and the next-to-leading-order QCD evolution on F₂^p(x, Q²) which gives a very good fit to the available data in the (x, Q²)-plane. It is shown that the free neutron to proton structure functions ratio can be extracted from the corresponding EMC ratios for ³He and ³H mirror nuclei by using the self-consistent iteration procedure and the results are in good agreement with the other theoretical models as well as the present available experimental data and especially the projected data expected from the proposed 11GeV Jefferson Laboratory in the near future.     

Unpolarized structure functions and the parton distributions for nucleon in an independent quark model

Considering the nucleon as consisting entirely of its valence quarks confined independently in a scalar-vector harmonic potential; unpolarized structure functions F ₁(x, μ ²) and F ₂(x, μ ²) are derived in the Bjorken limit under certain simplifying assumptions; from which valence quark distribution functions u _v(x, μ ²) and d _v(x, μ ²) are appropriately extracted satisfying the normalization constraints. QCD-evolution of these input distributions from a model scale of μ ²=0.07 GeV² to a higher Q ² scale of Q ₀ ² =15 GeV² yields xu _v(x, Q ₀ ² ) and xd _v(x, Q ₀ ² ) in good agreement with experimental data. The gluon and sea-quark distributions such as G(x, Q ₀ ² ) and q _s(x, Q ₀ ² ) are dynamically generated with a reasonable qualitative agreement with the available data; using the leading order renormalization group equations with appropriate valence-quark distributions as the input.     

QCD analysis of structure functions in terms of Jacobi polynomials

A new method of QCD-analysis of singlet and nonsinglet structure functions based on their expansion in orthogonal Jacobi polynomials is proposed. An accuracy of the method is studied and its application is demonstrated using the structure functionF ₂(x, Q ²) obtained by the EMC Collaboration from measurements with an iron target.     

The longitudinal structure function F L(x, Q 2) and the gluon distribution G(x, Q 2) at low x

We obtain a relation between the longitudinal structure function F _L(x, Q ²), F ₂(x, Q ²) and G(x, Q ²) at small x, using the formalism recently reported by one of the authors [2]. We also obtain a relation between F _L(x, Q ²), F ₂(x, Q ²) and its slope (dF ₂(x, Q ²))/(dlnQ ²). This provides us with the determination of the longitudinal structure function F _L(x, Q ²) from F ₂(x, Q ²) data and hence extract the gluon distribution G(x, Q ²).     

Azimuthal asymmetry and ratio R = FL/FT as probes of the charm content of the proton

We study two experimental ways to measure the heavy-quark content of the proton: using the Callan-Gross ratio R(x,Q ²) = F _L /F _T = and/or azimuthal cos(2φ) -asymmetry in deep inelastic lepton-nucleon scattering. Our approach is based on the perturbative stability of the QCD predictions for these two quantities. We resume the mass logarithms of the type α _s ln(Q ²/m ²) and conclude that heavy-quark densities in the nucleon can, in principle, be determined from data on the Callan-Gross ratio and/or azimuthal asymmetry. In particular, the charm content of the proton can be measured in future studies at the proposed Large Hadron-Electron (LHeC) and Electron-Ion (EIC) Colliders.     

On the extraction of elastic neutron electromagnetic form factors from highQ 2 D(e,e′) scattering

The problem of extraction of the neutron magnetic form factor from highQ ² D(e, e′) data is considered. We calculate the inelastic contribution to the cross section using two models of the EMC effect and find that the extracted value ofG _Mn(Q ²) is not sensitive to the deuteron structure forQ ²≦6 GeV². At the same time accurate data atQ ²>10 GeV² and x≧ l would enable to establish presence of the EMC type effect for the deuteron.     

Interference of Electromagnetic and Weak Interactions at High Energies and Neutral-Current μe Universality

A review is given on three types of experiments which recently detected the interference of electromagnetic and weak interactions at high energies in the reactions eD₂ → eX (SLAC, 1979), e⁺e⁻ → μ⁺μ⁻ (PETRA/PEP, 1981–83) and μ±C→μ±X (BCDMS, 1982). Asymmetry formulae are explicitely derived using the quark-parton model and the SU(2) × U(1) standard theory. With particular emphasis on the deep inelastic muon scattering experiment, the corresponding experiments are described and their results summarized. Combined fits to the 1983 asymmetry and νe data verify completely the muon-electron universality of the weak neutral current interaction giving for the vector and axial-vector coupling constants v_e = 0.02 ± 0.06, a_e = −0.54 ± 0.03 (electrons) and v_μ = −0.05 ± 0.16, a_μ = −0.51 ± 0.05 (muons).     

On the perturbative stability of the QCD predictions for the ratio R=FL/FT in heavy-quark leptoproduction

We analyze the perturbative and parametric stability of the QCD predictions for the Callan–Gross ratio, R(x,Q ²)=F _L /F _T , in heavy-quark leptoproduction. We consider the radiative corrections to the dominant photon–gluon fusion mechanism. In various kinematic regions, the following contributions are investigated: exact NLO results at low and moderate Q ²≲m ², asymptotic NLO predictions at high Q ²≫m ², and both NLO and NNLO soft-gluon (or threshold) corrections at large Bjorken variable x. Our analysis shows that large radiative corrections to the structure functions F _T (x,Q ²) and F _L (x,Q ²) cancel each other in their ratio R(x,Q ²) with good accuracy. As a result, the NLO contributions to the Callan–Gross ratio are less than 10% in a wide region of the variables x and Q ². We provide compact LO predictions for R(x,Q ²) in the case of low x ≪1. A simple formula connecting the high-energy behavior of the Callan–Gross ratio and low-x asymptotics of the gluon density is derived. It is shown that the obtained hadron-level predictions for R(x→0,Q ²) are stable under the DGLAP evolution of the gluon distribution function. Our analytic results simplify the extraction of the structure functions F ₂ ^c (x,Q ²) and F ₂ ^b (x,Q ²) from measurements of the corresponding reduced cross sections, in particular at DESY HERA.     

The Q<Superscript>2</Superscript> dependence of polarized and unpolarized proton structure functions in the relativistic quark exchange framework

In this article we intend to discuss the evolution of polarized and unpolarized structure functions in the (x,Q²) plane. We analyze the proton data on the spin dependence asymmetry A₁(x,Q²), by making the dynamical assumption that at low resolution energies, the hadrons consist only of valence quarks and the scaling violation of F₂(x,Q²) at low x comes only from the gluons density. While the sea quark and the gluon distributions are calculated using the inverse Mellin technique and the various moments of the valence quarks, the valence quark distribution itself is obtained from the relativistic quark-exchange model. A comparison is made with the corresponding available experimental data. Finally in agreement with the data, it is demonstrated that there is no significant Q²-dependence of asymmetry A₁(x,Q²) for x ranging 0.014 ≤ x ≤ 0.25. Received: 11 September 1999 / Revised version: 8 December 1999     

Q 2 dependence of the measured asymmetry A 1: A test of the Bjorken sum rule

We analyze the proton and deutron data on the spin-dependent asymmetry A ₁(x, Q ²), supposing that the DIS structure functions g ₁(x, Q ²) and F ₃(x, Q ²) have a similar Q ² dependence. As a result, we have found that Λ ₁ ^p −Λ ₁ ⁿ =0.190±0.038 at Q ²=10 GeV² and Λ ₁ ^p −Λ ₁ ⁿ =0.165±0.026 at Q ²=3 GeV²; these values are in the best agreement with the Bjorken sum rule predictions. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 1, 9–14 (10 January 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Measurement of the magnetic formfactor of the deuteron forQ 2=0.5 to 1.3 (GeV/c)2 by a coincidence experiment

Elastic electron deuteron scattering was measured at the Bonn 2.5 GeV Electron-Synchrotron using a two spectrometer coincidence technique. Data were taken at values of the four momentum transfer squaredQ ²=0.50, 0.60, 0.78, 1.00, and 1.3 (GeV/c)² at electron scattering angles θ _e =77.5° to 139.0° in order to separate the magnetic dipole formfactorF _M (Q ²) from the electric formfactorF _E (Q ²). Experimental cross sections are compared to theoretical predictions and to measurements of other laboratories. The results indicate that contributions from meson exchange currents are not negligible in thisQ ² region.     

Strangeness in the nucleon: neutrino–nucleon and polarized electron–nucleon scattering

After the EMC and subsequent experiments at CERN, SLAC and DESY on the deep inelastic scattering of polarized leptons on polarized nucleons, it is now established that the Q²=0 value of the axial strange form factor of the nucleon, a quantity which is connected with the spin of the proton and is quite relevant from the theoretical point of view, is relatively large.In this review, we consider different methods and observables that allow one to obtain information on the strange axial and vector form factors of the nucleon at different values of Q². These methods are based on the investigation of the neutral current induced effects such as the P-odd asymmetry in the scattering of polarized electrons on protons and nuclei, the elastic neutrino (antineutrino) scattering on protons and the quasi-elastic neutrino (antineutrino) scattering on nuclei. We discuss in detail the phenomenology of these processes and the existing experimental data.     

A phenomenological analysis of the longitudinal structure function at small <Emphasis Type="Italic">x</Emphasis> and low <Emphasis Type="Italic">Q</Emphasis><Superscript>2</Superscript>

The longitudinal structure function in deep-inelastic scattering is one of the observables from which the gluon distribution can be unfolded. Consequently, this observable can be used to constrain the QCD dynamics at small x. In this work we compare the predictions of distinct QCD models with the recent experimental results for F _L(x,Q ²) at small x and low Q ² obtained by the H1 Collaboration. We focus mainly on the color dipole approach, selecting those models which include saturation effects. Such models are suitable at this kinematical region and also resum a wide class of higher-twist contributions to the observables. Therefore, we investigate the influence of these corrections to F _L in the present region of interest.Received: 23 June 2004, Revised: 13 July 2004, Published online: 14 September 2004     

On the rise of the proton structure function F2 towards low x

A measurement of the derivative (∂ lnF₂/∂ lnx)_Q²≡−λ(x,Q²) of the proton structure function F₂ is presented in the low x domain of deeply inelastic positron–proton scattering. For 5×10⁻⁵x0.01 and Q²1.5 GeV², λ(x,Q²) is found to be independent of x and to increase linearly with lnQ².