An introduction to the Generalized Parton Distributions

The recently introduced concepts of Generalized Parton Distributions (GPD) are reviewed in an introductory and phenomenological fashion. These distributions provide a rich and unifying picture of the nucleon structure. Their physical meaning is discussed. The GPD are in principle measurable through exclusive deeply virtual production of photons (DVCS) or of mesons (DVMP). Experiments are starting to test the validity of these concepts. First results are discussed and new experimental projects presented, with an emphasis on this program at Jefferson Lab.Received: 30 September 2002, Published online: 22 October 2003PACS: 12.38.-t Quantum chromodynamics - 13.60.-r Photon and charged-lepton interactions with hadrons - 14.20.Dh Properties of protons and neutrons     

Deeply virtual compton scattering from the neutron with CLAS and CLAS12

Generalised Parton Distributions (GPDs) offer an insight into the three-dimensional structure of the nucleon and its internal dynamics, relating the longitudinal momentum of quarks to their transverse position. A very effective means of accessing GPDs is via measurements of cross-sections and polarisation-asymmetries in Deeply Virtual Compton Scattering (DVCS). In particular, the beam-spin asymmetry (BSA) in DVCS from the neutron is especially sensitive to angular momentum of the up- and down-quarks, and its measurement therefore has potential to shed important light on the puzzle of nucleon spin. We present a preliminary extraction of BSA from a recent experiment using a 6 GeV electron beam and the CLAS detector at Jefferson Laboratory and introduce the Central Neutron Detector to be integrated with CLAS12 for the exclusive measurement of neutron DVCS at 11 GeV, made possible by the Jefferson Lab upgrade.     

Particle multiplicities in lead-lead collisions at the CERN large hadron collider from nonlinear evolution with running coupling corrections

We present predictions for the pseudorapidity density of charged particles produced in central Pb-Pb collisions at the LHC. Particle production in such collisions is calculated in the framework of k(t) factorization. The nuclear unintegrated gluon distributions at LHC energies are determined from numerical solutions of the Balitsky-Kovchegov equation including recently calculated running coupling corrections. The initial conditions for the evolution are fixed by fitting Relativistic Heavy Ion Collider data at collision energies square root[sNN]=130 and 200 GeV per nucleon. We obtain dNch(Pb-Pb)/deta(square root[sNN]=5.5 TeV)/eta=0 approximately 1290-1480.     

Isospin mixing in the nucleon and 4He and the nucleon strange electric form factor

In order to isolate the contribution of the nucleon strange electric form factor to the parity-violating asymmetry measured in 4He(e-->],e')4He experiments, it is crucial to have a reliable estimate of the magnitude of isospin-symmetry-breaking (ISB) corrections in both the nucleon and 4He. We examine this issue in the present Letter. Isospin admixtures in the nucleon are determined in chiral perturbation theory, while those in 4He are derived from nuclear interactions, including explicit ISB terms. A careful analysis of the model dependence in the resulting predictions for the nucleon and nuclear ISB contributions to the asymmetry is carried out. We conclude that, at the low momentum transfers of interest in recent measurements reported by the HAPPEX Collaboration at Jefferson Lab, these contributions are of comparable magnitude to those associated with strangeness components in the nucleon electric form factor.     

Single π~0 electro-production in the resonance region with CLAS

We report the analysis status of single π~0 electroproduction in the resonance region to study the electromagnetic excitation of the nucleon resonances. The study is aimed at understanding of the internal structure and dynamics of the nucleon. The experiment was performed using an unpolarized cryogenic hydrogen target and 2.0 and 5.8 GeV polarized electron beam during the e1e and e1-6 run periods with CLAS at Jefferson Lab. The new measurements will produce a data base with high statistics and large kinematic coverage for the hadronic invariant mass (W) up to 2.0 GeV in the momentum transfer (Q~2) range of 0.3-6.0 GeV~2. Preliminary results will be presented and compared with the various model calculations.     

Nucleon spin structure

The present status of the spin of the nucleon is reviewed. The focus will be on inclusive double-spin asymmetry measurements in electron-nucleon (³He) scattering. Recent results from Jefferson Lab will be presented as well as their impact on the transition regime between hadronic and partonic degrees of freedom in the nucleon spin structure.     

Exclusive electroproduction and the quark structure of the nucleon

The natural interpretation of deep inelastic scattering is in terms of hard scattering on QCD constituents of the target. We examine the relation between amplitudes measured in exclusive lepto-production and the quark content of the nucleon. We show that in the Bjorken limit, the natural interpretation of amplitudes measured in these hard exclusive processes is in terms of the quark content of the meson cloud and not the target itself. In this limit, the most efficient representation of these exclusive processes is in terms of leading Regge amplitudes.     

Exclusive meson production at HERMES

Hard exclusive production of mesons in deep-inelastic scattering allows one to probe the so-far unknown Generalized Parton Distributions (GPDs) of the nucleon. The HERMES experiment has measured several different observables in exclusive meson production by scattering the 27.6GeV HERA lepton beam off an internal fixed gaseous target. Recent results on exclusive π ⁺, ρ ⁰ and pion pair production will be presented.     

J/ψ-N center of mass energy dependence of nuclear absorption effect on J/ψ production

In this paper, the J/ψ nuclear absorption effect is studied at RHIC and LHC energies with the EKS98 shadowing parameterizations. By assuming that the J/ψ absorption cross section, σ abs , increases with the charmonium-nucleon (J/ψ-N) center of mass energy, s J/ψN , it is found that σ abs should depend on x F (or y) at a certain center of mass energy per nucleon pair,s , especially at LHC energies. The theoretical results with the x F (or y)-dependence of the absorption effect are in good agreement with the experiment data from PHENIX in d-Au collisions and the predicted results will be examined by the forthcoming experimental data from LHC in d-Pb collisions. Finally, we also present baseline calculations of cold nuclear matter effects on J/ψ production in nucleus-nucleus (A-A) collisions and find that the x F (or y)-dependence of absorption effect is very small at both RHIC and LHC energies in A-A collisions.     

The N~* physics program at Jefferson Lab

Recent measurements of nucleon resonance transition form factors with CLAS at Jefferson Lab are discussed. The new data confirm the assertion of the symmetric constituent quark model of the Roper as the first radial excitation of the nucleon. The data on high Q~2 nπ~+ production better constrain the branching ratios β_(Nπ) and β_(Nη). For the first time, the longitudinal transition amplitude to the S_(11)(1535) was extracted from the nπ~+ data. Also, new results on the transition amplitudes for the D_(13)(1520) resonance are presented showing a rapid transition from helicity 3/2 dominance seen at the real photon point to helicty 1/2 dominance at higher Q~2. I also discuss the status of the search for new excited nucleon states.     

Investigation of the focusing of a 50-GeV proton beam using a new crystal device

Bent crystals are used at large accelerators to deflect particle beams for extraction and collimation. Not only the deflection but also the focusing of beams by bent crystals can be required for recently formulated proposals for investigations at the Large Hadron Collider (LHC) with a fixed target. The experimental results on the focusing of a 50-GeV proton beam with a new crystal device, which can be used in a circulating beam of a large accelerator such as the LHC, have been reported.     

Study of spin sum rules (and the strong coupling constant at large distances)

We present recent results from Jefferson Lab on sum rules related to the spin structure of the nucleon. We then discuss how the Bjorken sum rule with its connection to the Gerasimov-Drell-Hearn sum, allows us to conveniently define an effective coupling for the strong force at all distances.     

Photoproduction and rescattering of polarized hyperons in deuterium

Excited states of hadrons are essential for understanding confinement and non-perturbative QCD. Constituent quark models are successful in describing the first excited nucleon (N ^*) states in each partial wave, but predict more states than have been observed experimentally. Diquark correlations have been suggested as one explanation for these “missing” states. Recent advances in both theory (coupled-channels calculations) and experiment (high-statistics polarization measurements) offer new tools for resolving this question. The g13 experiment at Jefferson Lab, completed in June 2007, forms an important part of this effort. It used linearly and circularly polarized photons and a deuteron target to study N ^* states produced on the neutron, primarily through their decays into kaons and hyperons. The self-analyzing property of the Λ is ideally suited for this purpose. The general nature and exceptional size of the data set will, however, produce a wide range of results, including opening a new window on the study of hyperon-nucleon interactions through rescattering processes.     

The role of the pion cloud in the interpretation of the valence light-cone wavefunction of the nucleon

The pion cloud renormalises the light-cone wavefunction of the nucleon which is measured in hard, exclusive photon-nucleon reactions. We discuss the leading twist contributions to high-energy exclusive reactions taking into account both the pion cloud and perturbative QCD physics. The nucleon’s electromagnetic form-factor at high Q² is proportional to the bare nucleon probability Z and the cross-sections for hard (real at large angle or deeply virtual) Compton scattering are proportional to Z². Our present knowledge of the pion-nucleon system is consistent with Z = 0.7 ± 0.2. If we apply just perturbative QCD to extract a light-cone wavefunction directly from these hard exclusive cross-sections, then the light-cone wavefunction that we extract measures the three valence quarks partially screened by the pion cloud of the nucleon. We discuss how this pion cloud renormalisation effect might be understood at the quark level in terms of the (in-)stability of the perturbative Dirac vacuum in low energy QCD.     

Study of excited nucleon states at EBAC: status and plans

We present an overview of a research program for the excited nucleon states in Excited Baryon Analysis Center (EBAC) at Jefferson Lab. Current status of our analysis of the meson production reactions based on the unitary dynamical coupled-channels model is summarized, and the N~* pole positions extracted from the constructed scattering amplitudes are presented. Our plans for future developments are also discussed.     

LHC能区的部分子分布函数

大型强子对撞机(LHC)能探测到核子中很小x的动力学区域.在此动力学区域部分子的密度很大,根据高扭度修正过的AP演化方程(MDAP方程),分析了此区域的部分子饱和问题.发现在LHC能区不会出现饱和现象,但部分子分布会由于高扭度效应而明显被抑制,出现部分饱和现象.根据MDAP演化方程,还对LHC能区的部分子分布进行了预言     

Coulomb and photo cross sections for nucleon emission from relativistic O projectiles

Coulomb cross sections for nucleon emission out of ¹⁶O projectiles scattered with laboratory energies of 2.1, 60 and 200 GeV/nucleon on various target nuclei are calculated in first-order perturbation theory by using the corresponding photo cross sections. The photo cross sections are obtained with an 1-particle-1-hole basis in the giant resonance region and with the quasi-deuteron model up to photon energies of 140 MeV. Whereas the 2.1 GeV/nucleon results agree well with the experimental data points, the 60 and 200 GeV/nucleon cross sections are roughly one quarter lower than the measured ones, because also photons with energies higher than 140 MeV contribute at these incident energies.     

COMPASS-II

On December 1st 2010 the proposal of the COMPASS-II Experiment [1] has been approved by the CERN Research Board. After almost ten years of important results achieved by the COMPASS Collaboration in both nucleon spin physics, with the use of muon beam, and hadron spectroscopy, using hadron beams, this second phase offers now a unique chance to address in the very near future newly opened QCD-related challenges, at very moderate upgrade cost, thanks to the versatility of the COMPASS apparatus [2]. This implies mainly study of chiral perturbation theory (ChPT), by measuring the pion polarizability through Primakoff reaction; generalized parton distributions (GPDs), by measuring exclusive deeply virtual compton scattering (DVCS) and hard exclusive meson production (DVMP); transverse momentum dependent parton distributions (TMDs) in single-polarised pion-induced Drell-Yan muon production and in SIDIS on a liquid hydrogen target (in parallel to DVCS). An overview of the COMPASS-II proposal is presented here, with a main focus on the new upcoming investigation of the nucleon structure via the Drell-Yan and DVCS processes.     

Unpolarized azimuthal asymmetries in SIDIS at COMPASS

The study of the spin structure of the nucleon and of the effects due to the quarks transverse momentum are part of the scientific program of COMPASS, a fixed target experiment at the CERN SPS. The azimuthal modulations which appear in the cross-section of SIDIS off unpolarised targets give insight on the intrinsic momentum structure of the nucleon and on the possible correlation between transverse spin and transverse momentum of the quarks. We present the results for the amplitudes of the cos(?), cos(2?), and sin(?) modulatuions (where ? is the azimuthal hadron angle in the gamma-nucleon system) obtained from the COMPASS data collected with a 160 GeV/c positive muon beam impinging on a deuteron target. The amplitudes are measured for both positive and negative hadrons, and the results on the dependence of the relevant kinematical variables obtained after a multi dimensional analysis are also presented.     

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.