GDH 2000

The following sections are included:

• Foreword

• CONTENTS

The history of spin and anomalous magnetic moment is full of puzzles and "crises" from the first observations in the 1920's to the present day. The Gerasimov-Drell-Hearn sum rule connects the anomalous magnetic moment with the helicity dependent cross section for photoproduction, and as such checks the internal consistency of our understanding of the nucleon spin structure. Various generalizations of the sum rule have been proposed for the case of virtual photons, thus interpolating from the real photon point to deep inelastic scattering. A series of recent and newly proposed experiments with beam and target/recoil polarization will study this transition between the coherent spin-dependent response and the incoherent response of the partons in the scaling region.

Following the idea of the quark-hadron duality we present, within the constituent quark model approach, the relations between different bremsstrahlung weighted integrals of the nucleon resonance amplitudes and/or cross sections and correlation functions of the quark dipole moments in the nucleon ground state. These functions are of interest for checking the detailed quark-configuration structure of the nucleon state vector. Some applications of this approach in the meson sector are made, and the role of meson degrees of freedom in the electromagnetic baryon observables is briefly discussed.

The structure functions and have been measured over the range 0.014 < x < 0.9 and 1 < Q² < 40 GeV² using deep-inelastic scattering of 48 GeV longitudinally polarized electrons from polarized protons and deuterons at SLAC. From a NLO QCD fit to all available data we find at Q² = 5 GeV², in agreement with the Bjorken sum rule prediction of 0.182±0.005. A rough estimate of Δσ^γp and Δσ^γn for an average photon energy of about 25 GeV is given based on inclusive photoproduction data from the same experiment. A recently submitted proposal to measure Δσ^γp and Δσ^γn for 5 < k < 40 GeV is discussed. The results will probe the high energy convergence of the proton and neutron GDH sum rules. The proposed experiment will use coherent bremsstrahlung, polarized NH₃ and ND₃ targets, and large calorimeters to measure final state hadrons.

The Q² dependence of the generalised Gerasimov-Drell-Hearn(GDH) integral for the proton has been measured in the range 1.2 GeV² < Q² < 12 GeV². The contributions of the nucleon-resonance and deep-inelastic regions to this integral have been evaluated separately.

I summarize the theoretical predictions for the spin–dependent nucleon polarizabilities based on chiral effective field theory approaches.

Results of the recently developed unitary isobar model (MAID) are presented for helicity amplitudes, spin asymmetries, structure functions and relevant sum rules for real and virtual photons in the resonance region. Our evaluation of the energy-weighted integrals is in good agreement for the proton but shows big discrepancies for the neutron.

As first topic, the GDH sume rule is discussed in the context of a more general class of sum rules associated with the various contributions to the total photoabsorption cross section for target and beam polarization. Then I address the question of whether the GDH sum rule for the neutron can be determined from the one for the deuteron. It appears that this will not be possible in a simple manner. The spin response of the deuteron is calculated including contributions from the photodisintegration channel and from coherent and incoherent single pion production as well, and the GDH integral is evaluated up to a photon energy of 550 MeV. The photodisintegration channel converges fast enough and gives a large negative contribution, essentially from the ¹S₀ state near threshold and its absolute size is about the same than the sum of proton and neutron GDH values. It is only partially cancelled by the single pion production contribution. But the incoherent channel has not reached convergence at 550 MeV.

We review some important aspects of the deep inelastic scattering spin-dependent structure function g₂. We examine its role in the strong Q² dependence of the generalized Gerasimov-Drell-Hearn sum rule, which involves g₁, the other spin-dependent structure function. Our analysis involves other relevant spin-dependent sum rules. We also discuss an improved positivity bound on the transverse asymmetry A₂, related to g₂, which leads to some new positivity constraints for quark distributions, at the leading twist level.

The generalized GDH sum rule has the potential of becoming a show-case of how perturbative QCD and effective low energy hadronic descriptions match at a scale of roughly Q² = 0.5 GeV². Coming from the QCD side the crucial question is the control of higher twist terms which determine down to which Q² a QCD description is sensible. The status of the OPE for the relevant higher twist terms is reviewed and it is extended to include cat-ear terms. Some numerical estimates from lattice QCD are presented and some general properties are discussed. The general conclusion is that higher twist effects are very small, such that the Q²-dependence is dominated by the elastic contribution. This should allow for a smooth connection to low energy models.

In May 1998, the GDH experiment has started in its data taking to measure the helicity dependence of total and partial photon nucleon cross sections. Circularly polarized photons from the tagged photon facility of the Mainz MAMI microtron were used together with longitudinally polarized nucleons in a frozen-spin target. The outgoing particles were detected in the large acceptance detector DAPHNE complemented with forward components to increase its angular acceptance. First preliminary results in the energy range from 200 up to 800 MeV are presented.

The helicity dependence of the γp → nπ⁺ and γp → pπ⁰ channels have been measured for incident photon energies from pion threshold to 800 MeV. We used the large acceptance detector DAPHNE with additional forward components, a newly developed frozen-spin target, and the tagged circularly polarized photon beam facility of the MAMI accelerator in Mainz. Preliminary results for the polarized total and differential cross sections of both single-pion channels are compared with partial wave analyses of HDT and SAID.

New preliminary data for the helicity dependent double pion photoproduction on the proton are presented in combination with the predictions from the Regge Plus Resonances model (RPR). The RPR model gives a fair description for and predicts the contribution of the double pion channels to the GDH sum rule and to the spin polarisability γ₀.

During the GDH experiment at MAMI, helicity-dependent photoproduction cross-section differences σ_3/2 – σ_1/2 have been measured on the proton. In addition to the partial channels Nπ and Nη we have extracted the cross-section differences for the three possible Nππ isospin channels to get the full set of helicity-dependent data in the range between ππ threshold and 800 MeV photon energy. The partial Nπ channels have to be reliably separated in order to avoid backgrounds. Methods are presented here and first preliminary results are shown for the helicity-dependent double-pion photoproduction for and .

The experimental test of the Gerasimov-Drell-Hearn sum rule is being performed at the electron accelerators MAMI in Mainz and ELSA in Bonn by the international GDH-Collaboration. First results of the measurements on the proton within the low energy range in Mainz have been published³. The setup of the experiment at ELSA and especially the GDH-Detector have been tested successfully by measurements of several unpolarized total cross sections. Moreover, the cross section off hydrogen has been determined as the difference of a CH₂- and a C-target in order to verify the efficiency of the detector as well as the analysis procedure for doubly polarized measurements of differences with butanol. The polarized electron beam achieved high polarization values which were determined reliably with the GDH-Møller-Polarimeter. For a few hours of beam time in June 2000 doubly polarized data have been taken. The full setup showed an excellent performance. Hence, the polarized experiment for the range of higher energies (680 to 3100 MeV) in Bonn at ELSA is ready to commence.

The resources of TUNL include polarized beams of p, d and n. In addition, the new HIGS project is providing intense, 100% linearly polarized γ-ray beams below 50 MeV. Some features of these beams will be discussed. Recently, several of these beams have been used in preliminary efforts to measure the GDH sum rule integrand near photo-disintegration threshold for d and ³He. The results of these studies will be discussed. Intense beams of circularly polarized γ rays at energies below 50 MeV are being developed at HIGS, and will be used to perform direct measurements of the GDH sum-rule integral for d and ³He below 50 MeV.

Recent improvements in producing proton and deuteron solid polarized targets for particle physics experiments are discussed. The emphasis is put on progress with frozen spin targets for double polarization experiments with tagged photon beams. A new frozen spin technique made possible the first experiments towards a test of the Gerasimov-Drell-Hearn sum rule at the Mainz electron accelerator MAMI.

Scintillating polarized targets are now routinely available: blocks of 18×18×5 mm scintillating organic polymer, doped with TEMPO, polarized dynamically in a field of 2.5 T in a vertical ³He-⁴He dilution refrigerator. A 19 mm diameter plastic lightguide transports the scintillation light from the sample in the mixing chamber to a photomultiplier outside the cryostat.

A solid, polarized HD target has been developed for the measurement of double-polarization observables in the Δ resonance region. This new polarized target technology, combined with the upgrade to the LEGS photon beam energy and the large acceptance spectrometer, SASY, provides a unique facility for studying the spin structure of the nucleon below 500 MeV. With the addition of magnetic analysis to SASY, a complete set of pion production observables on the proton and the deuteron will be obtained.

We discuss the polarized ³He target used at Jefferson Lab - Hall A for experiments E-94010 and E-95001. The experiments measured polarized cross-sections and asymmetries, respectively. We discuss the two issues relevant for extracting these observables from the data, namely polarimetry and target density.

We consider Compton scattering off the proton within a formalism of fixed-t subtracted dispersion relations which can be used to extract the proton polarizabilities from data with a minimum of model dependence. In addition we discuss the possibility to probe the proton structure via the use of higher-order polarizabilities.

The following sections are included:

• Experiments on Compton Scattering

• Extraction of the Polarizabilities

• Unpolarized vs. Double Polarized Experiments

• Summary

• References

We present a calculation of the fourth-order (NLO) contribution to spin-dependent Compton scattering in heavy-baryon chiral perturbation theory, and we give results for the four spin polarisabilities. No low-energy constants, except for the anomalous magnetic moments of the nucleon, enter at this order. The NLO contributions are as large or larger than the LO pieces, making comparison with experimental determinations questionable. We address the issue of whether one-particle reducible graphs in the heavy baryon theory contribute to the polarisabilities.

I discuss a generalization of the concept of nucleon spin-polarizabilities and present an overview of the available theoretical predictions up to now for these elusive but interesting structure parameters of the nucleon.

The importance of the s-wave photoproduction multipoles close to threshold for the GDH sum rule and the spin polarizability γ₀ is discussed. Generalizations of these quantities as functions of the photon 4-momentum Q² are studied in the context of the phenomenological model MAID. Comparisons of the predictions of MAID and chiral perturbation theory are given.

The Virtual Compton Scattering experiment in the threshold regime performed at MAMI at Q² = 0.33 GeV² seems to indicate a large contribution of the spin-dependent polarizabilities which is predicted by the chiral models. This study can be pursued with a double polarization experiment in order to disentangle the scalar and spin-dependent polarizabilities.

We report on a dispersion relation formalism for the virtual Compton scattering (VCS) reaction on the proton, which for the first time allows a dispersive evaluation of 4 generalized polarizabilities. The dispersion formalism provides a new tool to analyze VCS experiments above pion threshold, thus increasing the sensitivity to the generalized polarizabilities of the nucleon.

I shall discuss three experiments which form part of a comprehensive physics program aimed at the study of the spin structure of the neutron using a polarized ³He target and a polarized beam at JLab in Hall A. Results from the first experiment performed to evaluate the Gerasimov-Drell-Hearn (GDH) extended sum rule are presented and future approved measurements are discussed. The main goal of these experiments is to bridge our understanding of the strong interaction in the large Q² regime where quarks and gluons are the relevant degrees of freedom to the low Q² regime where constituent quarks and mesons seem to be more adequate for a description of the nucleon properties.

The preliminary results obtained at the Jefferson Lab using CLAS, the spectrometer of Hall B, the polarized electron beam and the proton and deuteron polarized target are presented. The simultaneous measurement of inclusive and exclusive reactions was possible thanks to the large acceptance of the detector. The extraction of single and double spin asymmetries on wide Q² and W intervals is underway. The impact of these data on the GDH sum rule as well as on the study of the spin structure of the nucleon resonances is discussed.

An experiment with polarized electron beam on a polarized proton target is in progress in Hall B at CEBAF using CLAS (Cebaf Large Acceptance Spectrometer). This experiment provides data in the nucleon-resonance region at moderate and low Q² (0.2 < Q² < 1.75 GeV²), and allows for the first time the extraction of single and double polarization asymmetries in the ep → eπ⁺n channel. The measured asymmetries, expressed in term of bilinear combinations of the helicity amplitudes, have been demonstrated to be extremely sensitive to the baryonic structure and will allow a test of different models of the nucleon resonances. The analysis of the CLAS data is in progress and preliminary results in the measurement of double spin asymmetries are presented.

The status of baryon resonance electroproduction at high momentum transfer is presented in the overall context of exclusive reactions. Alternate theoretical descriptions, including constituent quarks, generalized parton distributions, and PQCD are discussed as momentum transfers vary from small (large λ) to large (small λ) values. The role of helicity and polarization asymmetries is considered. The Δ(1232) is discussed as a test case. The future of the high Q² program at Jefferson Lab in Halls C and B, as the beam energy increases to 12 GeV is also discussed.

We report on the experiment E94-010 recently completed at Jefferson Lab. The experiment studies the spin structure of the neutron. To this end we have measured polarized inclusive cross sections and asymmetries. In this report we give an overview of the experiment and how we control our systematic uncertainty. Preliminary results on the and spin structure functions are given.

The polarized beam for the GDH experiment at Mainz was produced by the recently built compact source set-up in MAMI Hall A. The task of achieving longitudinal spin polarization at the bremstarget was achieved by small energy variations of MAMI at 525 and 855 MeV. Stable operation was achieved for the whole beam time with an average polarization of 75%. Results of ongoing research for even higher beam polarization are presented.

A pulsed 50 kV inverted gun of polarized electrons, optimized for a reliable operation for future experiments at the stretcher ring ELSA, was set into operation. Due to operation in space charge limitation a current of 100 mA in a rectangular 1µs long electron puls is produced. Using a Be-InGaAs/Be-AlGaAs superlattice photocathode P = 80 % and QE = 0.2 % could be obtained. The performance of the gun, the transfer line and the results of first measurements are described in this report.

A polarized high energy photon beam line was constructed by means of Compton back scattering of laser light against 8 GeV electrons circulating in the SPring-8 storage ring. The intensity is 2.5 × 10⁶/s at maximum for the full energy spectrum up to 2.4GeV, at the electron current of 100mA with the laser power of 5W. Interesting physics programs to be performed at the beam line were submitted as letters of intents. One of them is the GDH experiment where the helicity dependent total photo-absorption cross-section will be measured from 1.8 GeV to 2.8 GeV. Preparation of the experiment are in progress.

The GRAAL facility, with its polarized γ-ray beam and 4π multi-detector, is a privileged tool to study the nucleon resonances in the energy range from E_γ = 500 MeV to 1500 MeV. The construction of a new polarized HD target, HYDILE, is in progress at Orsay and preliminary results are promising. The high polarization and quality of such a target makes possible a number of double polarization experiments at GRAAL including a measurement of the GDH Sum Rule.

With the addition of two Septum Magnets to the HRS spectrometers in Hall A at Jefferson Lab it will be possible to perform experiments at very forward scattering angles (6°) allowing measurements at very low Q². An experiment on the Q² dependence of GDH in the range of 0.02 to 0.5 (GeV/c)² will take data in the fall of 2001. This experiment will allow to obain the the slope of the GDH sum rule at so low Q² that a resonable extrapolation to the real photon point can be obtained. The spin structure functions will be measured from threshold region to the resonance region and beyond. The comparison of the ³He and the neutron GDH sum rule will be used to study how good is the assumption that the polarized ³He target is almost a polarized neutron target and to test the ³He models.

Spin structure functions and asymmetries for inclusive scattering of 2.5 GeV polarized electrons off polarized deuterium have been measured as part of the EG1 program in Jefferson Lab's Hall B. These data improve significantly our knowledge of the spin-dependent nucleon structure in the resonance region and at low to moderate Q². This paper presents preliminary results for the inclusive asymmetry (with some contribution from ) and the Ellis-Jaffe integral of the spin structure function .

We present a detailed analysis of resonance contributions in the context of higher twist effects in the moments of the proton spin structure function g₁. For each of these moments, it is found that there exists a characteristic Q² region in which (perturbative) higher twist corrections coexist with (non-perturbative) resonance contribution of comparable magnitude.

The twist–3 and 4 matrix elements describing power corrections to the lowest moments of the nucleon spin structure functions can be estimated in an instanton–based description of the QCD vacuum. The twist–3 matrix element d⁽²⁾ is suppressed in the packing fraction of the instanton medium and expected to be numerically small, in agreement with the recent analysis of the E155 and E155x data for g₂(x, Q²). The twist–4 matrix element f⁽²⁾ is parametrically large. We present numerical estimates of f⁽²⁾ for both the flavor–nonsinglet and singlet case.

We argue that flavour asymmetry of polarized antiquarks in the nucleon is a sensitive probe of the non-perturbative mechanisms responsible for generating of sea distributions.

A qualitative QCD analysis and a quantitative model calculation are given to show that the constituent quark model remains a good approximation even with the nucleon spin structure revealed in polarized deep inelastic scattering being taken into account.

A parameterization of the real and the virtual photon spin dependent cross section for the proton and neutron is presented. A Regge inspired parameterization is obtained from global fits to the cross section data derived from the spin asymmetries measured in deep inelastic scattering. An accurate description of the data is provided and a reliable prediction for the photo-production through a smooth Q²-transition is given. New precise data from HERMES and SLAC experiments are in excellent agreement with our model. The parameterization is used to evaluate the contribution above the resonance region to the Gerasimov-Drell-Hearn sum rule for real and virtual photons. The main result is the large high-energy and multi-hadron contribution to the GDH sum rule, particularly in the isovector channel. Taking into account this large contribution, together with preliminary data from Mainz, the GDH sum rule seems to be fulfilled.

Recent Jlab data of the differential cross section of the reaction p(e, e′p)π⁰ in the invariant mass region of 1.1 < W < 1.4 GeV at four-momentum transfer squared Q² = 2.8 and 4.0 (GeV/c)² are re-analyzed with two models, both of which giving an excellent description of most of the existing pion electroproduction data below W < 1.5 GeV. The ratios E₁₊/M₁₊ extracted with these two models show, starting from a small and negative value at real photon point, a clear tendency to change sign with increasing Q².

The GDH sum rule is discussed for the Δ(1232) resonance. It is shown that apart from ordinary excitations to higher-energy states, the sum rule contains a large negative contribution due to de-excitation into the nucleon state. Therefore, a fulfillment of the sum rule assumes a strong coupling of Δ⁺ and Δ⁰ to resonances of . Calculations performed in quark models suggest that D₁₅(1675) may be such a resonance. However, its strength is found to be not sufficient for bringing the GDH sum rule to a theoretically expected positive magnitude.

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

The subject of low energy polarized Compton scattering form the proton, which is characterized by phenomenological spin-polarizabilities, is introduced and connection is made to new theoretical and experimental developments which were reported to this meeting.

Recent progress on the polarized targets and polarized beams at Bonn, Brookhaven, Jefferson Lab, Mainz and PSI were reported in the parallel sessions. Summary of the progress is presented here.

The following sections are included:

• Author Index

• PROGRAM

• List of participants