Lepton Scattering, Hadrons and QCD

The following sections are included:

• Foreword

• Contents

In this talk we highlight recent lattice calculations of the nucleon form factors and structure functions.

An improved method for the chiral extrapolation of lattice QCD calculations of moments of structure functions from heavy quark masses to the physical region is presented. This extrapolation is based on the general constraints of the chiral symmetry of QCD and is able provide an excellent fit to the lattice data and the experimental values for each moment. Using the extrapolated moments, the Björken x dependence of the u - d structure function is also investigated.

Theoretical calculations suggest charge symmetry violation [CSV] for parton valence distributions of a few percent. Precision measurements of structure functions in muon and neutrino DIS set rather stringent experimental limits on CSV. Previous data appeared to show substantial CSV effects in the nucleon sea; this effect has largely disappeared upon re-analysis of CCFR data. We suggest further experiments which could test parton CSV.

We report on recent work concerning the effect which the change in vacuum structure (negative energy Dirac sea), in the presence of a confining scalar field, has on the nucleon structure functions and parton distributions. Using the Dirac equation in 1+1 dimensions, we show that distortions in the Dirac sea are responsible for part of the violation of the Gottfried sum rule – i.e., part of the flavor asymmetry in the proton sea. Our basic argument is that, even if isospin is an exact symmetry, the presence of a confining potential changes the vacuum structure, and inevitably leads to a violation of SU(2) flavour symmetry in a hadron with a different number of valence u and d quarks. The same mechanism also leads to a prediction for and .

Parton distributions for the pion are studied in a chiral quark model characterized by a quark propagator for which a spectral representation is assumed. Electromagnetic and chiral symmetry constraints are imposed through the relevant Ward-Takahashi identities for flavoured vertex functions. Finiteness of the theory, requires the spectral function to be non-positive definite. Straightforward calculation yields the result that the pion structure function becomes one in the chiral limit, regardless of the details of the spectral function. LO and NLO evolution provide a satisfactory description of phenomenological parameterizations of the valence distribution functions but fails to describe gluon and sea distributions.

I discuss the physical interpretation of GPDs in the limit ξ = 0, where the t dependence contains information about the distribution of partons in the transverse plane. GPDs thus allow a simultaneous determination of the longitudinal momentum and transverse position of partons in the infinite momentum frame, which also sheds some light on the physical interpretation of Ji's angular momentum sum rule.

Preliminary results for exclusive electroproduction of vector mesons, pseudoscalar mesons and real photons from HERMES are presented. Different observables like cross sections and single spin azimuthal asymmetries are studies. Exclusive processes are connected with the recent formalism of the Generalized Parton Distributions.

An evaluation of soft pion production associated with Deeply Virtual Compton Scattering is presented. A Low Energy Theorem is built to calculate the amplitudes, and its validity for soft pion production is discussed. Comparative results for typical experimental set-ups are shown.

An experimental review of the nucleon spin structure functions g₁ and g₂, as measured in deep inelastic scattering of polarized leptons by polarized nucleons, is presented. Particular emphasis is given to the theoretical interpretation of the spin structure functions, to recent experiments at CERN, SLAC and DESY, and to the presentation and discussion of the available experimental data.

We review the nucleon's polarized structure functions from the viewpoint of gauge invariant, nonlocal light-cone operators in QCD. We discuss a systematic treatment of the polarized structure functions and the corresponding parton distribution functions. We also address a question of what information on the structure of Nature will be obtained from the future polarized experiments. From this point of view, we will discuss the W^±γ production at RHIC polarized experiment.

We study the fragmentation of a transversely polarized quark into a non collinear (k_⊥ ≠ 0) spinless hadron and the fragmentation of an unpolarized quark into a non collinear transversely polarized spin 1/2 baryon. These nonperturbative properties are described by new spin and k_⊥ dependent fragmentation functions and are revealed in the observation of single spin asymmetries. Recent data on the production of pions in polarized semi-inclusive DIS and older data on Λ polarization in unpolarized p–N processes are considered: these new fragmentation functions can describe the experimental results and the single spin effects in the quark fragmentation turn out to be surprisingly large.

We present the first calculation of the complete NLO QCD corrections to the production of heavy flavors with longitudinally polarized hadrons. Predictions for the extraction of the gluon helicity density at RHIC using this reaction are made and their theoretical uncertainties are briefly discussed. We also mention the potential of polarized photoproduction of heavy flavors at the EIC project.

After a brief review on flavour symmetry breaking (FSB) in the unpolarized nucleon sea, we discuss theoretical predications for FSB in the polarized nucleon sea from meson cloud and 'Pauli blocking'.

At high enough energies asymptotic freedom guarantuees the deep inelastic scattering cross sections to be calculated as nearly free electron-quark scattering. However, confinement guarantees that the experimentally observed final states particles are hadrons. Low-energy quark-hadron duality suggests that hadronic cross sections, when averaged over an appropriate energy range, nevertheless coincide with the naive leading-twist quark-gluon calculations. Deep inelastic inclusive scattering shows that scaling at modest Q² and ν already arises from very few resonance channels. This is reflected by the striking agreement (< 10%) between data in the nucleon resonance region and the deep inelastic (W² > 4 GeV²) region for Q² > 0.5 (GeV/c)², known as Bloom-Gilman duality. Electron-hadron scattering allows for further investigation of quark-hadron duality by virtue of its ability to select resonances, by tagging with either spin or flavor.

We discuss the origin of Bloom-Gilman duality and the relationship between resonances and scaling in deep-inelastic scattering. A simple quantum mechanical model is used to illustrate the essential features of Bloom-Gilman duality at low Q². As an application of local duality, we present model-independent relations between structure functions at x ~ 1 and elastic electromagnetic form factors.

We study the Q² dependence of large x data on F₂ from Jefferson Lab, SLAC, and BCDMS, with the aim of providing a perturbative-QCD (pQCD) based, quantitative verification of Bloom and Gilman's local duality relation. We find that most of the data in the resonance region (with invariant mass W² = Q²(1/x - 1) + M² ≤ 4 GeV²) can be described within a pQCD based picture, similarly to the large W² data, including large x resummation contributions, target mass corrections, and relatively small size residual power corrections. We uncover however a possible breakdown of the twist expansion in the N - Δ transition region which, by affecting the initial evolution of parton distributions, bears consequences on pQCD analyses at large x and very large Q². A dynamical model for local duality is proposed which accounts for the Q² dependence unravelled in the first part of our work.

Lattice-based investigations of two fundamental QCD quantities are described, namely the gluon and quark propagators in Landau gauge. We have studied the Landau gauge gluon propagator using a variety of lattices with spacings from a = 0.17 to 0.41 fm to explore finite volume and discretization effects. We also introduce the general method of "tree-level correction" to minimize the effect of lattice artefacts at large momenta. We demonstrate that it is possible to obtain scaling behavior over a very wide range of momenta and lattice spacings and to explore the infinite volume and continuum limits of the Landau-gauge gluon propagator. These results confirm the earlier conclusion that the Landau gauge gluon propagator is infrared finite. We study the Landau gauge quark propagator in quenched QCD using two forms of the -improved propagator with the Sheikholeslami-Wohlert quark action with the nonperturbative value for the clover coefficient c_sw and mean-field improvement coefficients in our improved quark propagators. We again implement an appropriate form of tree-level correction. We find good agreement between our improved quark propagators. The extracted value of the infrared quark mass in the chiral limit is found to be 300 ± 30 MeV. We conclude that the momentum regime where the transition from nonperturbative to perturbative QCD occurs is Q² ≃ 4 GeV².

Model calculations of parton distributions are one of the ways to connect our knowledge of physics at low energy scales with the high energy scales where α_QCD is small. There now exist a number of these calculations giving qualitative agreement with experimental data. We present a best-fit analysis for the valence u and d quark distributions calculated in the MIT bag model and in a chirally symmetric extension of the bag model. This analysis yields best-fit model parameters in agreement with other low energy fits, and provides new constraints on the parameters governing the pion cloud of the nucleon.

The measurement of the elastic form factors is a key ingredient to any complete understanding of the internal structure of the nucleons, and ultimately of the strong force. Precise data are essential to impose stringent tests on any QCD-based theory. The electromagnetic interaction provides a unique tool to investigate these form factors. In elastic electron scattering off a proton, the electron interacts with the nucleon exchanging a virtual photon. The electron-photon interaction is fully understood from QED, hence making the hadron vertex the only unknown of the reaction…

We review recent progress in the understanding of the functional dependence of hadron masses and electromagnetic properties on quark mass. This is a fascinating area in which there has been a very productive interplay between hadron models, chiral perturbation theory and lattice QCD. The results lead one to expect to be able to deduce quite accurate hadron properties from the next generation of supercomputers, with speeds of tens of Tera-flops, rather than hundreds.

Charge symmetry between the light u and d quarks in octet baryons provides relations among various quark-sector contributions to baryon magnetic moments which may be used to gain information on the strange quark contribution to the nucleon magnetic moment, . In analyzing these relations, it is important to consider the nonanalytic contributions to baryon magnetic moments arising from the meson cloud. In this report we consider both the π- and K-meson contributions to baryon magnetic moments. We find that the contribution from is large and plays a pivotal role in the final determination of . With the inclusion of the cloud, we find is definitely negative with .

We discuss the calculation of electromagnetic observables in the context of Light-Front Dynamics. We show why one should be very careful to clearly identify the non-physical contributions to any approximate calculation which arise from the explicit breaking of covariance in Light Front Dynamics.

We summarize recent progress in soft QCD modeling based on the set of Dyson–Schwinger equations truncated to ladder-rainbow level. We pay particular attention to electromagnetic elastic and transition form factors of the pion. This covariant approach accommodates quark confinement and implements the QCD one-loop renormalization group behavior. The dressed quark propagators are compared to the most recent lattice-QCD data.

The nucleon is described as a bound state of a quark and an extended diquark. Hereby the notion "diquark" refers to the modelling of separable correlations in the two–quark Green's functions. Binding of quarks and diquarks takes place via an exchange interaction. Fully Poincaré covariant nucleon amplitudes are calculated for free constituent propagators as well as for dressed propagators which parameterise confinement. The corresponding results for space–like form factors differ quantitatively but not qualitatively for various ansätze for the propagators. These results do not allow one to draw definite conclusions on the permissibility of different dressing functions. Results for kaon photoproduction, on the other hand, exclude a whole class of constituent propagators.

This talk reviews some recent results and future plans for measurements of the hadron spectrum. These measurements emphasize the mass and width of resonant states with particular quantum numbers. We also address the decay dynamics of some of these states. Shortcomings of the presently existing data set are pointed out, and experiments in preparation are discussed.

A succinct review of the QCD gap equation and dynamical chiral symmetry breaking; their connection with Bethe-Salpeter equations and resolving the dichotomous nature of the pion; the calculation of the pion's valence-quark distribution; and first results for the π-exchange contribution to the γN → ωN cross-section, which is important in the search for missing nucleon resonances.

I describe how confinement and constituent representations may arise in QCD in the Coulomb gauge. Implications for studies of phenomena related to low energy gluonic excitations, in particular hybrid mesons, are discussed.

We describe a regularization-independent method for studying a renormalizable field theory nonperturbatively through its Dyson-Schwinger equations. Using QED₄ as an example, we show how the coupled equations determining the non-perturbative fermion and photon propagators can be written entirely in terms of renormalized quantities, which renders the equations manifestly finite in a regularization-independent manner. As an illustration of the technique, we apply it to a study of the fermion propagator in quenched QED₄ with the Curtis-Pennington electron-photon vertex.

We discuss how the inclusion of singular gauge fields in the partition function for QCD can lead to a domain-like picture for the QCD vacuum by virtue of specific conditions on quantum fluctuations at the singularities. With a simplified model of hyperspherical domain regions with interiors of constant field strength we calculate the basic parameters of the QCD vacuum, the gluon condensate, topological susceptibility, string constant and quark condensate, and briefly discuss confinement of dynamical quarks and gluons.

We study glueball properties at finite temperature using SU(3) lattice QCD at the quenched level with an anisotropic lattice. We use a tree-level Symanzik O(a²) improved action. We present our preliminary results which shows the slight reduction of the scalar glueball mass near T_c.

A model for the quantum effective description of the vacuum structure of thermalized SU(3) Yang-Mills theory is proposed. The model is based on Abelian projection leading to a Ginzburg-Landau theory for the magnetic sector. The possibility of topologically non-trivial, effective monopole fields in the deconfining phase is explored. These fields are assumed to be Bogomol'nyi-Prasad-Sommerfield saturated solutions along the compact, Euclidean time dimension. Accordingly, a gauge invariant interaction for the monopole fields is constructed. Motivated by the corresponding lattice results the vacuum dynamics is assumed to be dominated by the monopole fields. A reasonable value for the critical temperature is obtained, and the partial persistence of non-perturbative features in the deconfining phase of SU(3) Yang-Mills theory, as it is measured on the lattice, follows naturally.

Utilizing conventional many-body techniques, an effective QCD Hamiltonian formulated in the Coulomb gauge is approximately diagonalized. This approach preserves chiral symmetry yet generates constituents with dynamical mass confined through a linear potential with slope specified by lattice gauge theory. The experimental meson and lattice glueball spectra are reasonably described and exhibit Regge trajectories consistent with observation including the Pomeron. A fully relativistic, three quasiparticle calculation for hybrid mesons reinforces alternative theoretical models and predicts the lightest hybrid states are near but above 2 GeV. This strongly suggests the recently observed J^PC = 1^-+ exotics at 1.4 and 1.6 GeV are of a different, perhaps four quark, structure. Charmonium predictions now resolve the overpopulation of J/Ψ states relative to observation. Extensions and preliminary results for low energy ππ scattering are also discussed.

At very high energies, the high parton densities (characterized by a semi-hard saturation scale Λ_s) ensure that parton distributions can be described by a classical effective field theory with remarkable properties analogous to those of spin glass systems. This color glass condensate (CGC) of gluons also provides the initial conditions for multi-particle production in high energy nuclear collisions. In this talk, we briefly summarize recent theoretical and phenomenological progress in the CGC approach to small x physics. In particular, we discuss recent numerical work on the real time gluodynamics of partons after a nuclear collision. The implications of this work for the theoretical study of thermalization in nuclear collisions and on the phenomenological interpretation of results of the recent RHIC experiments are also discussed.

Experimental results from HERA on the production of leading nucleons in e⁺ p collisions are reviewed. The data cover a large kinematic range from photoproduction to deep inelastic scattering. The protons and neutrons are produced with low transverse momentum and carry a large fraction of the incoming proton's energy (x_L > 0.6). The data are compared to hadroproduction experiments and to the predictions of particle-exchange models. Some implications of the data for the structure of the pion are also discussed.

Nuclear effects have been studied at HERMES in inclusive and semi-inclusive reactions in D, ³He and ¹⁴N unpolarized targets using a 27.5 GeV positron beam. In the inclusive case, cross section ratios for deep-inelastic scattering from ¹⁴N and ³He with respect to D have been measured. The data provide evidence for an A-dependence of the ratio R = σ_L/σ_T of longitudinal to transverse DIS cross sections at low x and low Q². In the semi-inclusive case, the influence of the nuclear medium on the production of charged hadrons has been studied. The differential multiplicity of charged hadrons and pions from ¹⁴N relative to that from D has been measured as a function of the virtual photon energy ν and the fraction z of this energy transferred to the hadron. A substantial reduction of the multiplicity ratio R_M at low ν and high z is observed. Moreover, a significant difference of R_M is found for positive and negative hadrons.

We study nuclear shadowing for the flavor non-singlet structure function . The violation of isospin symmetry for the ³He and ³H wave functions induces, via nuclear shadowing terms, the charge symmetry breaking for and which significantly increases, at small x, over and leads to the divergence of the Gottfried integral.

In the first part of this work we investigate the structure functions, in particular their flavor dependencies, and static properties of the nucleon in a relativistic three-body approach to the NLJ model, using a simple quark-diquark approximation to the full Faddeev method. In the second part we consider the problem of nuclear matter stability in chiral models like the NJL model.

The following sections are included:

• A "Next-Generation" Facility for Partonic Physics

• Semi-Inclusive Measurements of Parton Structure

• Hard Exclusive Processes at a Collider

• Hadronic Physics with Nuclei

• References

The following sections are included:

• LIST OF PARTICIPANTS