Sensitivity of the pQCD deuteron structure to the nucleon form factors

We discuss the applicability of pQCD to the elastic scattering of electrons on protons and deuterons. We analyze the Q²-dependence of the reduced deuteron form factor, taking into account the recent data on the electric proton form factor and we find that the value of the QCD-scale parameter Λ differs essentially from the value Λ = 0.1 GeV, previously found using the dipole parametrization of the electromagnetic nucleon form factors G_E and G_M. Moreover, the predicted scaling behavior of the reduced deuteron form factor cannot be recovered in the Dirac and Pauli representations for the nucleon electromagnetic form factors. Received: 14 October 2002 / Accepted: 12 November 2002 / Published online: 11 March 2003 RID="a" ID="a"Permanent address: National Science Center KFTI, 310108 Kharkov, Ukraine. RID="b" ID="b"e-mail: etomasi@cea.fr Communicated by V.V. Anisovich     

On the polarization of the final nucleon in NC elastic \nu _\mu (\bar \nu _\mu )-N scattering

New short baseline neutrino experiments open new possibilities of high precision study of different neutrino processes. We present here results of the calculation of the polarization of final nucleon in elastic NC $\nu _\mu (\bar \nu _\mu )$ -nucleon scattering. In a numerical analysis the sensitivity to the different choices of the axial and axial strange form factors is examined. Measurements of the polarization of the final proton in elastic e-p scattering drastically changed our knowledge about the electromagnetic form factors of the proton. From measurement of the nucleon polarization in the NC elastic scattering a new additional information about the axial G _A (Q ²) and the strange axial G ^s _A (Q ²) form factors of the nucleon could be inferred.     

Logarithmic corrections and soft photon phenomenology in the multipole model of the nucleon form factors

We analyzed the presently available experimental data on nucleon electromagnetic form factors within a multipole model based on dispersion relations. A good fit of the data is achieved by considering the coefficients of the multipole expansions as logarithmic functions of the momentum transfer squared. The superconvergence relations, applied to this coefficients, makes the model agree with unitary constraints and pQCD asymptotics for the Dirac and Pauli form factors. The soft photon emission is proposed as a mechanism responsible for the difference between the Rosenbluth, polarization and beam-target asymmetry data. It is shown that the experimentally measured cross-sections depend not only on the Dirac and Pauli form factors, but also on the average number of the photons emitted. For the proton this number is shown to be different for different types of experimental measurements and then estimated phenomenologically. For the neutron the same mechanism predicts that the data form different types of experiments must coincide with high accuracy. A joint fit of all the experimental data reproduce the Q²-dependence with the accuracy χ²/dof = 0.86 . Predictions of the model, that 1) the ratios of the proton form factors G _E/G _M are different for Rosenbluth, polarization and beam-target asymmetry experiments and 2) similar ratios are nearly the same for neutron, can be used for experimental verification of the model.     

Nucleon form factors of the isovector axial-vector current

The theoretical and experimental status of the isovector axial-vector current form factors G _A(q ²) and G _P(q ²) of the nucleon is reviewed. We also describe a new calculation of these form factors in manifestly Lorentz-invariant chiral perturbation theory (ChPT) with the inclusion of axial-vector mesons as explicit degrees of freedom.     

Strange quarks in the nucleon sea

The HAPPEX Collaboration measured parity-violating electron scattering from ⁴He$(e, e)$and H(e, e) in 2004 and 2005 for Q ²≤0.11GeV^2. Results for the strange-quark contributions to the electromagnetic form factors of the nucleon from the 2004 data will be reviewed. Preliminary results from the 2005 data, which have significantly greater statistical precision, are G _E ^s = 0.004±0.014_stat±0.013_syst for Q ² = 0.0772GeV^2 from the helium data and G _E ^s +0.088G _M ^s = 0.004±0.011_stat±0.005_syst±0.004_FF for Q ² = 0.1089GeV^2 from the hydrogen data.     

Extraction of the neutron charge form factor G<Superscript>n</Superscript><Subscript>E</Subscript>(Q<Superscript>2</Superscript>) from the charge form factor of deuteron G<Superscript>d</Superscript><Subscript>C</Subscript>(Q<Superscript>2</Superscript>)

We extract the neutron charge form factor G ⁿ _E(Q ²) from the charge form factor of deuteron G ^d _C(Q ²) obtained from T ₂₀(Q ²) data at 0≤Q ²≤ 1.717 (GeV/c)². The extraction is based on the relativistic impulse approximation in the instant form of the relativistic Hamiltonian dynamics. Our results (12 new points) are compatible with existing values of the neutron charge form factor of other authors. We propose a fit for the whole set (36 points) taking into account the data for the slope of the form factor at Q ² = 0. Received: 26 July 2002 / Accepted: 18 September 2002 / Published online: 4 February 2003 RID="a" ID="a"e-mail: krutov@ssu.samara.ru RID="b" ID="b"e-mail: troitsky@theory.sinp.msu.ru Communicated by V.V. Anisovich     

The ratio of the magnetic to the electric proton form factors in Quantum Chromodynamics

We propose a two parameter expression for the high momentum transfer behaviour of the ratio of proton form factors G_M(Q²)/Q_E(Q²) based on perturbation theory calculations in Quantum Chromodynamics. A fit to the present experimental data and its consistency with a previous fit to the high Q² behaviour of the Dirac form factor [1] is also discussed.     

Possible method for measuring the proton form factors in processes with and without proton spin flip

The ratio of the squares of the electric and magnetic proton form factors is shown to be proportional to the ratio of the cross sections for the elastic scattering of an unpolarized electron on a partially polarized proton with and without proton spin flip. The initial proton at rest should be polarized along the direction of the motion of the final proton. Similar results are valid for both radiative ep scattering and the photoproduction of pairs on a proton in the Bethe-Heitler kinematics. When the initial proton is fully polarized in the direction of the motion of the final proton, the cross section for the ep → ep process, as well as for the ep → epγ and γp → $ e\bar ep $ e\bar ep processes, without (with) proton spin flip is expressed only in terms of the square of the electric (magnetic) proton form factor. Such an experiment on the measurement of the cross sections without and with proton spin flip would make it possible to acquire new independent data on the behavior of G _E ²(Q ²) and G _M ²(Q ²), which are necessary for resolving the contradictions appearing after the experiment of the JLab collaboration on the measurement of the proton form factors with the method of polarization transfer from the initial electron to the final proton.     

Study of nucleon spin-dependent properties in the resonance region

In this paper, the spin-dependent structure functions of nucleon g ₁, and photoabsorption cross sections σ_1/2, σ_3/2 and σ_T in the resonance region are estimated based on the constituent quark model and the properties of the five phenomenological Breit-Wigner resonances P ₃₃(1232), S ₁₁(1535), D ₁₃(1520), P ₁₁(1440), and F ₁₅(1680). Our results are compared to the recent E143 data of the polarized structure functions g ₁(W ², Q ²) at points Q ²=0.5 GeV² and Q ²=1.2 GeV² and the data of the total inclusive photoabsorption cross sections. Received: 7 October 1997     

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).     

On the applicability of perturbative QCD to exclusive processes at currently available momentum transfer

We re-examine the problems connected with the end-point dominance in the calculation of exclusive processes in perturbative QCD. In a re-analysis we construct nucleon quark distribution amplitudes from the respective moments obtained from a QCD sum rule approach. These functions lead to acceptable values for the e.m. Dirac form factorsF ₁ ^p,n of the nucleon if effective gluon masses of ca. 300–600 MeV are included into the hard-scattering amplitude. In addition we also find a reasonable Q₂ — dependence of the proton form factor. The results point at the importance of the end-point k-dependence of distribution amplitude and hard-scattering amplitude in the calculation of exclusive processes.Work is supported by Deutsche Forschungsgemeinschaft (Ga 153-13-1) and partially by NATO (0581/87)     

A new approach to calculate the gluon polarization

We derive the Leading-Order (LO) master equation to extract the polarized gluon distribution G(x,Q ²)=xδg(x,Q ²) from polarized proton structure function, g^p₁(x,Q²)g^{p}_{1}(x,Q^{2}). By using a Laplace-transform technique, we solve the master equation and derive the polarized gluon distribution inside the proton. The test of accuracy which is based in our calculations on two different methods, confirms that we achieve to the correct solution for the polarized gluon distribution. To determine the polarized gluon distribution xδg(x,Q ²) more accurately, we only need to have more experimental data on the polarized structure functions, g₁^p(x,Q²)g_{1}^{p}(x,Q^{2}). Our result for polarized gluon distribution is in good agreement with some phenomenological models.     

The proton form factor measurements at Jefferson Lab, past and future

Use of the double-polarization technique to obtain the elastic nucleon form factors has resulted in a dramatic improvement of the quality of two of the four nucleon electromagnetic form factors, G _Ep and G _En . It has also changed our understanding of the proton structure, having resulted in a distinctly different Q ²-dependence for both G _Ep and G _Mp , contradicting the prevailing wisdom of the 1990’s based on cross section measurements, namely that G _Ep and G _Mp obey a “scaling” relation μG _Ep ～ G _Mp . A related consequence of the faster decrease of G _Ep revealed by the Jefferson Lab (JLab) polarization results was the disappearance of the early scaling F ₂/F ₁ ～ 1/Q ² predicted by perturbative QCD. In three experiments, GEp(1), GEp(2) and GEp(3), in Halls A and C at JLab, the ratio of the proton’s electromagnetic elastic form factors, G _Ep /G _Mp , was measured up to four momentum transfer Q ² of 8.5 GeV² with high precision, using the recoil polarization technique. The initial discovery that the proton form factor ratio measured in these three experiments decreases approximately linearly with four-momentum transfer, Q ², for values above ～ 1 GeV², was modified by the GEp(3) results, which suggests a slowing down of this decrease. There is an approved experiment, GEp(5), to continue these measurements to 15 GeV². A dedicated experimental setup, the super bigbite spectrometer (SBS), will be built for this purpose. It will be equipped with a new focal plane polarimeter to measure the polarization of the recoil protons. In this presentation, I will review the status of the proton elastic electromagnetic form factors, mention succinctly a number of theoretical approaches to describe results and show some features required for the future GEp(5) experiment.     

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.     

Nucleon form factors from a covariant quark core: Limits in their description

In treating the relativistic 3-quark problem, a dressed-quark propagator parameterization is used which is compatible with recent lattice data and pion observables. Furthermore 2-quark correlations are modeled as a series of quark loops in the scalar and axialvector channel. The resulting reduced Faddeev equations are solved for nucleon and delta. Nucleon electromagnetic form factors are calculated in a fully covariant and gauge-invariant scheme. Whereas the proton electric form factor G _E and the nucleon magnetic moments are described correctly, the neutron electric form factor and the ratio G _E/G _M for the proton appear to be quenched. The influence of vector mesons on the form factors is investigated which amounts to a 25% modification of the electromagnetic proton radii within this framework. Received: 16 April 2002 / Accepted: 29 August 2002 / Published online: 17 January 2003 RID="a" ID="a"Supported by a Feodor-Lynen fellowship of the Alexander-von-Humboldt foundation and the Australian Research Council. RID="b" ID="b"Address after April 30: MPI für Metallforschung, Heisenbergstr. 1, 70569 Stuttgart, Germany. RID="c" ID="c"e-mail: Reinhard.Alkofer@uni-tuebingen.de Communicated by A. Sch?fer     

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.