Quark-Hadron Duality and the Transition to PQCD

CONTENTS.

PREFACE.

Workshop Organization.

We consider some aspects of duality in lepton-hadron inelastic scattering, including how duality works when perturbative QCD is applicable, how to explain the peculiar behavior of the Δ(1232), and the finding that duality also appears in quantum mechanical models with confinement. We include an example of an application of duality-pertinent data to atomic physics, specifically to proton structure corrections to hydrogen hyperfine splitting.

The special features of the polarized structure functions g₁ and g₂ in relation to duality are briefly discussed, and the present knowledge about g₁ and g₂ in the resonance region is reviewed.

In a quantitative analysis of the neutron spin structure first moment in terms of its "twist expansion", the size of higher twists (twist-4) is found to be surprisingly small at Q²= 1 GeV² lending support to the concept of "global duality". The value of d₂ at Q²= 1 GeV² tends to suggest significant higher than twist-3 contribution (twist-5 and beyond). More precision data in the range 1 ≤ Q² ≤ 5 GeV² are needed for a definitive conclusion since the lattice prediction are at odds with the measured data at Q² = 4.8 GeV².

Results of recent analyses of electromagnetic structure functions in the resonance region suggest that duality-violating higher twists are small above Q² ~ 1 GeV². We analyze the systematics of local duality within a quark model framework for various modes of spin-flavor symmetry breaking. On the basis of these models we discuss expectations for the workings of duality in neutrino scattering.

A statistical model for the parton distributions in the nucleon has proven its efficiency in the global analysis of unpolarized and polarized deep-inelastic scattering data. This statistical approach involves only a few free parameters (eight) and has several characteristic features which will be recalled. Predictions for various QCD processes involving leptons and hadrons, are compared with recent experimental data from DESY, SLAC, FNAL, RHIC and Jefferson Lab. These new tests are very satisfactory and we will also discuss the prospect of this physical framework.

In order to remove a little of the mysticism surrounding the issue of strangeness in the nucleon, we present simple, physically transparent estimates of both the strange magnetic moment and charge radius of the proton. Although simple, the estimates are in quite good agreement with sophisticated calculations using the latest input from lattice QCD. We further explore the possible size of systematic uncertainties associated with charge symmetry violation (CSV) in the recent precise determination of the strange magnetic moment of the proton. We find that CSV acts to increase the error estimate by 0.003 μ_N such that .

We extract an effective strong coupling constant using low-Q² data and sum rules. Its behavior is established over the full Q²-range and is compared to calculations based on lattice QCD, Schwinger-Dyson equations and a quark model. Although the connection between all these quantities is not known yet, the results are surprisingly alike. Such a similitude may be related to quark-hadron duality.

Thomas Jefferson National Accelerator Facility experiment E01-012 measured the ³He spin structure functions and virtual photon asymmetries in the resonance region in the range 1.0 < Q² < 4.0 (GeV/c)². Our data, when compared with existing deep inelastic scattering data, can be used to test quark-hadron duality in g₁ and A₁ for ³He and the neutron. Preliminary results for are presented, as well as an overview of the experimental and theoretical developments.

Inclusive double spin asymmetries obtained by scattering polarized electrons off polarized protons and deuterons have been analyzed to address the issue of quark-hadron duality in the polarized spin structure functions and . A polarized electron beam, solid polarized NH₃ and ND₃ targets and the CEBAF Large Acceptance Spectrometer (CLAS) in Hall B were used to collect the data. The resulting and were averaged over the nucleon resonance energy region (M < W < 2.00 GeV), and three lowest lying resonances individually for tests of global and local duality.

A Jefferson Lab experiment proposal was discussed in this talk. The experiment is designed to measure the beam-target double-spin asymmetries in semi-inclusive deep-inelastic and reactions on a longitudinally polarized ³He target. In addition to the flavor non-singlet combination , in which the gluons do not contribute, will be determined with high precision to extract Δd_ν(x) independent of the knowledge of the fragmentation functions. The data will also impose strong constraints on quark and gluon polarizations through a global NLO QCD fit.

The RSS experiment ran in Hall C at Jefferson Lab and measured the proton and deuteron beam-target asymmetries for parallel and perpendicular target fields over a W range from pion threshold to 1.9 GeV at Q² ≈ 1.3 GeV². Preliminary results for the proton spin structure functions g₁ and g₂ are presented.

The origins of duality in pion-nucleon scattering are recalled. A simple model of vector-meson photoproduction is outlined based on vector-meson dominance. This gives an excellent description of data at small t and, analogously to pion-nucleon scattering, it can be concluded that vector-meson photoproduction also satisfies the original duality. The situation for vector-meson electroproduction is more complicated and it is argued that, in the kinematical domain acessible to HERMES and JLab, nonperturbative effects may be significant. This has implications for the study of generalized parton distributions in vector-meson electroproduction.

In this talk, we present the most recent data on charged pion photoproduction from nucleon at Jefferson Lab. These new data suggest a transverse momentum of ~ 1.2 (GeV/c) as the physical quantity governing the onset of the scaling behavior. We also present a new analysis of the proton-proton elastic scattering data and also of the photopion production data based on the generalized counting rule.

The onset of pQCD description of deuteron reactions with electromagnetic probes is examined. The deuteron two-body photodisintegration and the ed elastic scattering reactions are studied. Experimental cross section data are in agreement with the Constituent Counting Rule at relatively low energies, while Hadron Helicity Conservation seems to be not consistent with polarization measurements.

The exclusive production of baryon-antibaryon pairs in the collisions of two quasi-real photons has been studied using different detectors at e⁺e^- colliders. Results are presented for , , and final states. The cross-section measurements are compared with all the existing experimental data and with the analytic calculations based on the three-quark model, on the quark-diquark model, and on the handbag model.

Inclusive studies of nuclear photoabsorption have provided clear evidence of medium modifications in the properties of hadrons. However, the results have not been explained in a model independent way. A deeper understanding of the situation is expected from a detailed comparison of meson photoproduction from nucleons and from nuclei in exclusive reactions. Recent experimental results are presented.

Inclusive hadron production in deeply inelastic scattering off a large nucleus (DISA) involves parton propagation through the nuclear medium and hadronization which could start inside the nucleus. In most of the kinematic region accessible in high-energy DISA, the hadron formation time is much larger than the nuclear size. Therefore, leading hadron suppression in DISA can be described by modification of the parton fragmentation via multiple scattering and induced energy loss.

We investigate hadron production in deep inelastic lepton-nucleus scattering in the kinematic regime of the HERMES experiment. Our calculations are carried out in the framework of a BUU transport model which contains the Lund event generators PYTHIA and FRITIOF for the simulation of high-energy elementary interactions. For the first time we consistently use the complete four-dimensional information of the Lund string break up vertices as input for our transport theoretical studies of (pre)hadronic final state interactions. We compare our results with experimental HERMES data on charged hadron attenuation.

An informal overview geared towards experimental colleagues, focussed on ab initio calculations and results on quark gluon plasma and the hadronic phase at high temperature.

We report the calculation of the proton and neutron unpolarized structure functions using local duality for both neutrino and muon scattering, in the large x region. Our result indicate a possible violation of local duality at the nucleon pole for the case of neutrino scattering.

The size of higher twist corrections to the spin proton and neutron g₁ structure functions and their role in determining the polarized parton densities in the nucleon is discussed.

Higher twist effects in nucleon spin structure functions provide an opportunity to understand quark-quark and quark-gluon correlations in the nucleon. A series of experiments in Jefferson Lab Hall A has enabled the extraction of higher twist effects in the neutron with unprecedented precision.

The current status of deep inelastic scattering is briefly reviewed. We discuss future theoretical developments desired and measurements needed to further complete our understanding of the picture of nucleons at short distances.

We study both polarized and unpolarized proton structure functions in the kinematical region of large Bjorken x and four-momentum transfer of few GeV². In this region the phenomenon of parton-hadron duality takes place between the smooth continuation of the deep inelastic scattering curve and the average of the nucleon resonances. We present results on a perturbative-QCD analysis using all recent accurate data with the aim of extracting the infrared behavior of the nucleon structure functions.

I discuss two issues related to high "radial" excitations which attracted much attention recently: (i) chiral symmetry restoration in excited mesons and baryons, and (ii) universality of the ρ-meson coupling in QCD and AdS/QCD. New results are reported and a curious relation between an AdS/QCD formula and 1977 Migdal's proposal is noted.

Numerically large QCD scales were discussed first in connection with a number of phenomena mostly related to vacuum quantum numbers and 0^± glueball and quark channels. We present arguments regarding the possible role of the larger scale in diquarks important for low-energy hadron phenomenology. Good diquarks, i.e. the 0⁺ states of two quarks, are argued to have a two-component structure with one of the components peaking at distances several times shorter than a typical hadron size (a short-range core).

The AdS/CFT correspondence is a powerful tool to study the properties of conformal QCD at strong coupling in terms of a higher dimensional dual gravity theory. The power-law falloff of scattering amplitudes in the non-perturbative regime and calculable hadron spectra follow from holographic models dual to QCD with conformal behavior at short distances and confinement at large distances. String modes and fluctuations about the AdS background are identified with QCD degrees of freedom and orbital excitations at the AdS boundary limit. A description of form factors in space and time-like regions and the behavior of light-front wave functions can also be understood in terms of a dual gravity description in the interior of AdS.

We investigate for the light quark sector the possible corrections to the linear Regge trajectories by matching two-point correlators of quark currents to the Operator Product Expansion. We find that the allowed modifications to the linear behavior must decrease rapidly with the principal quantum number. After fitting the lightest states in each channel and certain low-energy constants the whole spectrum for meson masses and residues is obtained in a satisfactory agreement with phenomenology. The perturbative corrections to our results are discussed.

In the first section, the subject of Generalized Parton Distributions (GPDs) is briefly reviewed. Then, in the second section, we discuss duality considerations which can be used to constrain the parametrisation of the GPDs.

Hard exclusive leptoproduction of real photons and mesons provides access to the unknown Generalised Parton Distributions (GPD) of the nucleon which give a unified description of hadronic structure. Different observables, like cross sections, single-spin asymmetries or angular distributions for deeply virtual exclusive real photon and meson production have been measured at HERA (HERMES, H1 and ZEUS), CERN SPS (COMPASS) and JLab (CLAS). The recent experimental results will be reviewed and compared to the GPD expectations. Finally, prospects of future measurements will be presented.

The possible advantages of transverse polarized DIS for applications of QCD duality are analyzed. The status of Bloom-Gilman duality in QCD is discussed and its validity for the structure function g_T is deduced. The special role of this function is also manifested in the analysis of GGDH sum rules.

The extension of the statistical approach to the transverse degrees of freedhom explains a moltiplicative factor, we were obliged to introduce in a previous work to comply with experiment for the Fermi-Dirac functions of the light quarks. It is possible to get light antiquark distributions similar to the ones proposed there.

The plans for upgrading the CEBAF accelerator at Jefferson Lab to 12 GeV are presented. The research program supporting that upgrade is illustrated with a few selected examples. The instrumentation under design to carry out that research program is discussed.

A new hadron facility is under construction at Darmstadt: FAIR (Facility for Antiproton and Ion Research). This will upgrade the scientific opportunities available at the GSI laboratory with new radioactive and relativistic ion's beams and a new antiproton's machine. Some aspects of the scientific program accessible with the new antiproton beam, that will be addressed by the ANDA experiment, are here illustrated.

It has recently been suggested by the PAX collaboration that collisions of transversely polarized protons and antiprotons at the GSI-FAIR can be used to determine the nucleon's transversity densities from measurements of the double-spin asymmetry for the Drell-Yan process. The theoretical expectations for this observable are in the 0.3–0.4 range at the FAIR-HESR enrgies. PAX therefore proposes to build a polarized antiproton stored beam suitable for this measurament. Polarized antiprotons will be produced by spin filtering with an internal polarized gas target in a storage ring. The design and performance of the accelerator setup, and of the the detector will be briefly outlined.

I ascribe the origins of Bloom-Gilman duality in DIS to a separation of scales between the hard subprocess and soft resonance formation. The success of duality indicates that the subprocesses of exclusive form factors are the same as in DIS. The observed dominance of the longitudinal structure function at large x in πN → μ⁺μ^-X can explain why local duality works for DIS with a pion target. The failure of duality in semi-exclusive processes indicates that high momentum transfer t is not sufficient to make the corresponding subprocesses compact.

Workshop Program.

AUTHOR INDEX.

List of Participants.