GDH 2004

FOREWORD

CONTENTS

This year is the fiftieth anniversary of the origins of the GDH sum rule. The rule can be traced back to work on dispersion relations for Compton scattering in the 1950’s, and can be inferred under certain conditions from a paper by Gell-Mann, Goldberger and Thirring in 1954, among others. In this talk the author will describe how Compton scattering dominated his work in physics since 1959. This work involved not only the sum rule, but also his Ph.D. thesis and several related papers. It was also a catalyst for his career change from physics to computer science in the early 1970’s.

Dispersive sum rules, of which the Drell-Hearn-Gerasimov sum rule is a special example, are a consequence of rather general principles. On the one hand, they can be used to make tests of these fundamental principles, allowing to probe deep mysteries of nature. On the other hand, they can be used to access experimental observables that are otherwise impossible to measure, and thus providing excellent opportunities to learn about the physics of strongly interacting systems, such as nucleons and nuclei. I will use examples to illustrate these points.

I discuss the spin structure of the nucleon at low photon virtualities in the framework of a Lorentz–invariant formulation of baryon chiral perturbation theory. The structure functions of doubly virtual Compton scattering are calculated to one– loop accuracy. The role of the delta and other resonances is analyzed and first steps towards a covariant effective field theory with spin-3/2 fields are outlined. As an example, the quark mass expansion of the delta mass is discussed.

The GDH Sum Rule has not been investigated experimentally until recently. For the first time this fundamental sum rule is verified by the GDH-Collaboration with circularly polarized real photons and longitudinally polarized nucleons at the two accelerators ELSA and MAMI. The investigation of the response of the proton as well as of the neutron allows an isospin decomposition. Data from the resonance region up to the onset of the Regge regime are shown. The experimental approach will be presented as well as systematic uncertainties. The level at which the GDH Sum Rule for the proton has been verified is presented and estimates for the GDH integral for the neutron and the iso-vector case are given based on our new data.

The GDH sum rule connects ground state properties of the nucleon with helicity dependent cross sections. To investigate these cross sections on the deuteron, experiments have been carried out in the A2-Collaboration at the Mainz Microtron, Germany, in 1998 and in 2003, using circularly polarized photons on a polarized d-butanol target. A status report of the data analysis and latest results from the pilot experiment of 1998 are given.

We have measured the electron-³He longitudinal and transverse spin dependent inclusive cross sections , in the resonance region over a range of four-momentum transfer from 0.1 to 0.9 GeV². From this measurement, the spin dependent structure functions g₁(x), g₂(x) of ³He have been extracted and various moments of the neutron were evaluated. The integral of g₁(x) shows a smooth continuation from the existing high Q² data toward Q² ~ 0. And that of g₂(x) provided the first significant experimental evidence of the Burkhardt-Cottingham Sum Rule on the neutron in our measured Q² region. Spin polarizabilities of the neutron (γ₀ and δ_LT) were evaluated and compared with the existing chiral perturbation calculations and MAID model. Higher twist effect on g₂(x) was studied from d₂ moments and finally, color polarizabilities of the neutron were extracted from the combined data of the world and Jefferson Lab. Our new results seem to show small higher twist effects in the neutron with a possibility of quark-hadron duality down to Q² ~ 0.5 GeV².

A large program of spin structure function measurements is underway in Jefferson Lab’s Hall B. Of particular interest is the first moment of the spin structure function g₁, which goes through a rapid transition from the photon point (Q² = 0), where it is constrained by the Gerasimov-Drell-Hearn sum rule, to the deep inelastic limit where it is sensitive to the nucleon spin fraction carried by quarks. One can then study the transition from hadronic to quark degrees of freedom over the whole range of Q². We use polarized electrons incident on polarized NH₃ and ND₃ targets to study proton and deuteron spin observables in and above the resonance region. Using the Cebaf Large Acceptance Spectrometer (CLAS) and beam energies of 1.6, 2.4, 4.2 and 5.7 GeV, we are able to cover a wide kinematic range: 0.05 GeV² < Q² < 5.0 GeV² and W < 3.2 GeV. We will describe the experiment and present the GDH and Bjorken integrals using the 1.6 and 5.7 GeV data.

We present here recent progress on the experimental study of the neutron spin structure at Jefferson Lab Hall A. We focus on two precision experiments. The physics motivation and the experimental setup will be described first. Then we present results for the neutron spin asymmetry and results for spin-flavor decomposition of the nucleon spin in the valence quark region, and preliminary results for the neutron spin structure function at low Q².

Inclusive electron-nucleon scattering data from Jefferson Lab’s Hall B have been analyzed to test quark-hadron duality for the polarized structure function g₁(x, Q²) over a Q² range from 0.2 to 3.5 GeV²/c². Incident polarized electrons of energy 1.6 and 5.7 GeV were scattered by polarized ¹⁵NH₃ and ¹⁵ND₃ targets. The measured values of g₁(x, Q²) in the resonance region at Q² above 2.0 GeV²/c² appear to be equivalent to a fit of g₁(x, Q²) in the deep inelastic scattering region at high Q². A quantitative test comparing the ratio of the first moment in the resonance region to the first moment in the deep inelastic region is consistent with unity when Q² goes beyond 2.0 GeV²/c² but substantially departs from unity when Q² < 1.0 GeV²/c².

This is a review of the experimental and phenomenological knowledge of the spin dependent structure function g₁ at low values of x and Q².

Our knowledge on the nucleon spin structure has greatly improved over the last twenty years or so, but still many fundamental questions remain unsolved. I will try to review some of the puzzling aspects of the origin of the nucleon spin. I will emphasize the connection with several sum rules and, when using this tool, the relevance of some kinematic regions for testing them in the QCD dynamics framework.

An extensive experimental program to measure the spin structure of the nucleons is being carried out with the CLAS detector at Jefferson Lab using a longitudinally polarized electron beam incident on a longitudinally polarized target. Spin degrees of freedom offer new tools to explore the baryon structure and test the many theoretical approaches that attempt to characterize it, such as effective Lagrangian models and transverse momentum dependent parton distributions. I will present preliminary results for single and double spin asymmetries for exclusive π⁰, π⁺, and η electroproduction in the resonance region compared with unitary isobar and dynamical models, as well as ρ electroproduction for DIS kinematics. I will also report on an analysis of the semi-inclusive and exclusive channels where double and single spin asymmetries were used to study transverse momentum dependent parton distributions.

A high quality double polarization data set for the helicity dependence of the total and differential cross sections for both γp → Nπ channels in the Δ region has been obtained in the framework of the GDH experiment. The experiment, performed at the Mainz microtron MAMI, used a 4π detection system, a circularly polarized photon beam, and a longitudinally polarized frozen-spin target. The more recent results will be presented, with a particular emphasis on the second resonance region.

Strangeness production in the few GeV region has been investigated with a linearly polarized photon beam at LEPS. Our motivation is mainly a search for various exotic states. The status of our recent data, especially on ϕ meson and Θ⁺ baryon production, and the preparation status of the GDH experiment are presented.

Developments in lattice field theory and computer technology have led to dramatic advances in the use of lattice QCD to explore the quark structure of hadrons. This talk will describe selected examples, including structure functions, electromagnetic form factors, the nucleon axial charge, the origin of the nucleon spin, the transverse structure of the nucleon, and the nucleon to Delta transition form factor.

A brief experimental overview of the workshop is given, with emphasis on polarized targets from the experimental equipment perspective, and kinematic coverage, precision, and newly investigated channels from the experimental results perspective.

A large fraction of the world data on both polarized and unpolarized inclusive ep scattering at large Bjorken x lies in the resonance region where a correspondence with the deep inelastic regime, known as Bloom and Gilman’s duality, was observed. Recent analyses of the Q² dependence of the data show that parton-hadron duality is inconsistent with the twist expansion at low values of the final state invariant mass. We investigate the nature of this disagreement, and we interpret its occurrence in terms of contributions from non partonic degrees of freedom in a preconfinement model.

The 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 combined with existing deep inelastic data can be used to test quark-hadron duality on g₁ and A₁ for ³He and the neutron. The demonstration of duality for spin structure functions will enable the use of resonance data to study nucleon spin structure in the very high x_bj region. Preliminary results of will be presented as well as an overview of the experiment and theoretical developments.

Inelastic scattering using polarized nucleon targets and polarized charged lepton beams allows the extraction of the structure functions g₁ and g₂ which provide information on the spin structure of the nucleon. A program designed to study such processes has been underway in Jefferson Lab since 1998. 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 desired data. The measurements cover the resonance region with unprecedented detail and add significantly to the DIS data set at low to moderate Q² and moderate to high x. The measured electron asymmetries are analyzed to produce quantities of interest, such as the photon-nucleon asymmetry , the spin structure function and its first moment Γ₁.

The parity-conserving single-spin beam asymmetry of elastic electron-proton scattering is induced by an absorptive part of the two-photon exchange amplitude. We demonstrate that this asymmetry has logarithmic and double-logarithmic enhancement due to contributions of hard collinear quasi-real photons. An optical theorem is used to evaluate the asymmetry in terms of the total photoproduction cross section on the proton.

In a continuing study of irradiated polarized target materials, various samples have been subjected to irradiations with the 19 MeV electron beam at the MIRF facility at NIST. Previously, deuterated materials were investigated and the polarization results reported. In this paper we report on further investigations with deuterated materials and a first look at proton polarizations under the same conditions.

A solid, polarized HD target has been developed for the measurement of double-polarization observables in the Δ resonance region. Since the use of the first target in-beam in November 2001, dramatic improvements have been made to the in-beam and transfer cryostats and the NMR circuit has been redesigned and is well understood.

Nuclear spin-polarized ³He is often used as an effective polarized neutron target for nuclear physics experiments. Polarized helium-3 (³He) targets using spin-exheange optical pumping (SEOP) routinely achieve polarizations of ≈ 40%, which is well below the theoretical expectation of ≈ 70%. Hybrid SEOP using potassium (K) in addition to rubidium (Rb) has the potential to increase target performance. This is because K-³He spin exchange is up to an order of magnitude more efficient than Rb-³He spin exchange. Other proposed upgrades that are discussed include a large pumping chamber cell geometry and the use of combiner and homogenizer optical fibers. Using hybrid SEOP, we have polarized 3.3 liters of ³He to 43%, which to our knowledge is the largest volume of ³He polarized to ≥40%.

A frozen spin target for the CEBAF Large Acceptance Spectrometer (CLAS) is under construction for a series of experiments that scatter tagged, polarized photons from both longitudinally and transversely polarized protons. Compared to the polarized target previously used inside CLAS, the proposed frozen spin target will better utilize the spectrometer’s nearly 4π acceptance. The target material will be dynamically polarized at 5 T and 0.3 K and then cooled to about 0.05 K by a horizontal ³He/⁴He dilution refrigerator. The polarization will be preserved by internal superconducting coils providing 0.3−0.5 T.

Preliminary results on the beam asymmetry for the η and π° photoproduction off the quasi-free proton and the quasi-free neutron in the deuteron were obtained in the energy range 0.65-1.5 GeV of the incoming photon.

New preliminary results will be discussed for the target spin asymmetry in exclusive Deeply Virtual Compton Scattering(DVCS). The asymmetry is the result of interference between the DVCS and the Bethe-Heitler amplitude.

Asymmetries in beam charge, beam helicity and target polarization have been measured for hard exclusive electroproduction of photons, ρ° and π⁺ in HERMES. The asymmetries appear in the distribution of the photons or mesons in the azimuthal angle around the virtual photon direction, relative to the lepton scattering plane. Such asymmetries can constrain the Generalized Parton Distributions (GPDs) of the nucleon or nucleus. The experiment is performed at the DESY laboratory in Hamburg Germany, using 27.5 GeV positrons and electrons incident on hydrogen, deuterium and neon targets.

The experiments E00-110 and E03-106 [1] propose to measure the Deep Virtual Compton Scattering process (DVCS) ep → epγ and en → enγ in Hall A at Jefferson Lab with a 5.75 GeV longitudinally polarized electron beam. The exclusivity requires the High Resolution Spectrometer of the Hall A for the detection of the scattered electron (∆p/p = 10⁻⁴), an electromagnetic calorimeter for the detection of the real photon (σ/E < 5%) and a scintillator array for the detection of the third particle. A 1 GHz sampling system allows one to deal with pile-up as expected from running detectors at small angles and high luminosity L = 10³⁷ cm⁻² s⁻¹. We will describe the apparatus and will explain the method to extract GPDs and evaluate the contributions from higher twists from the measurement of the cross-section difference.

We present measurements of spin asymmetries in semi-inclusive processes in hard scattering kinematics using a 5.7 GeV electron beam and the CEBAF Large Acceptance Spectrometer (CLAS) at JLab. Scattering of longitudinally polarized electrons off an unpolarized liquid-hydrogen and off a polarized NH₃ targets was studied over a wide range of kinematics. Non-zero single-beam and single-target spin asymmetries have been observed in semi-inclusive pion production in hard-scattering kinematics (Q² > 1.2 GeV²,W² > 4 GeV²). Systematic studies of factorization of x and z dependences have been done for different spin-dependent and spin-independent observables. No significant x/z dependence has been observed within statistical uncertainties, which is consistent with factorization of hard scattering and fragmentation processes.

We report on an experimental determination of the Q²-dependence of the Bjorken sum using data from Jefferson Lab Hall A and Hall B in the range 0.16 < Q² < 1.1 GeV². A twist analysis is performed. Overall, the higher twist corrections are found to be small due to a cancellation between the twist 4 and 6 terms.

The generalized Baldin sum rule for virtual photon, an unpolarized analog of the generalized Gerasimov-Drell-Hearn sum rule, provides an unique way to investigate the transition between the perturbative QCD and hadronic descriptions of nucleon structure. We report on new measurements in Hall C at Jefferson Lab of the generalized Baldin integral for the proton at Q² of 0.3-4.0 GeV².

A reanalysis of all available world data on the longitudinal asymmetry A_|| is presented. The proton structure function g₁ was extracted within a unique framework of data inputs and assumptions. These data allowed for a reliable evaluation of moments of the structure function g₁ in the Q² range from 0.2 up to 30 GeV². The Q² evolution of the moments was studied in QCD by means of the Operator Product Expansion (OPE).

A measurement of the proton structure function g₁ for momentum transfer Q² in the range 0.01-0.5 GeV²/c² is planned in Hall B at Jefferson Lab using the CEBAF Large Acceptance Spectrometer (CLAS). The CEBAF polarized electron beam with energy between 1 and 3.2 GeV will scatter off a polarized solid state target. The outgoing electrons will be detected down to a minimum angle of ~5 degrees in CLAS thanks to a new gas Cherenkoy counter designed to optimize the detection efficiency and pion rejection in the operating conditions of this experiment. The proton spin structure function g₁ will be measured from the threshold region to the resonance region and beyond. The expected results will add high precision information on the nucleon spin response in kinematics where tests of Chiral Perturbation Theory are possible, and provide the data for an improved understanding of hadronic spin processes in the confinement regime.

A new set of experiments on meson photoproduction up to E_γ = 1.5 GeV is being planned for MAMI-C. It extends to higher energies the program carried out at MAMI-B. The experimental apparatus consists of the Crystal Ball multiphoton spectrometer together with TAPS as a forward wall, a central tracker based on a cylindrical wire chamber, and a scintillator barrel. This configuration provides a geometrical acceptance approaching 4π sterad and has good energy and angular resolution for photons as well as good angular resolution for charged particles. The detector will be equipped with a frozen-spin polarized target filled with , or . The new experimental program will focus on the helicity dependence of partial channels for investigating the properties of baryon resonances. We are also considering the possibility of measurements using a polarized target. It will substantially improve the quality of the existing neutron data.

The Gerasimov–Drell–Hearn sum rule was originally derived for real photon absorption and has been generalized to finite Q². Jefferson Lab experiment E97-110 has performed a precise measurement of the generalized GDH integral for both ³He and neutron and the neutron spin structure function moments in order to study their Q² dependence between 0.02 and 0.3 GeV². This range will allow us to test the dynamics of Chiral Perturbation Theory. The status and prospects of the data analysis will be discussed.

The High Intensity Gamma Source (HIγS) at the Duke Free Electron Laser Laboratory (DFELL) has created an opportunity to measure the spin polarizabilities of the neutron using polarized Compton scattering from a polarized ³He target. An experiment is being planned to measure the spin-dependent asymmetries from Compton Scattering from circularly polarized photons from a high-pressured polarized ³He gas target at quasi-elastic kinematics. The scattered photon and the recoil neutron will be detected in coincidence. The proposed beam energy is 140 MeV. We present the motivation and preliminary design of this experiment.

THe HIγS facility is presently undergoing an upgrade which will make measurements of the GDH integrand on the deuteron possible below pion threshold. The helical undulator system (OK-5) is presently being installed. This system will produce 100% circularly polarized γ rays. A booster injector is being built in Novosibirsk, and should be operating by mid-2006. This will eventually extend the energy of the HIγS γ-ray beam up to pion threshold. A frozen-spin target is also being constructed. The neutron detection system will consist of an upgraded version of the BLOWFISH neutron detector array. Experiments will begin in late 2006. Details of the experiment and a preliminary schedule will be presented.

We discuss the implications of a “constituent quark” structure of the nucleon for the leading (1/Q²−) power corrections to the spin structure functions, Our basic assumption is the presence of quark–gluon correlations in the nucleon wave function, whose size, ρ ~ 0.3 fm, is small compared to the nucleon radius, R (two–scale picture). We argue that in this picture the isovector twist–4 matrix element in the proton has a sizable negative value, , while the twist–3 matrix elements are small, . These findings are in agreement with the result of a QCD fit to g₁ world data, including recent neutron data from HERMES and Jefferson Lab Hall A, which gives .

The Gerasimov-Drell-Hearn integral I_GDH(Q²), and its relation to polarized nucleon structure functions, is discussed from the lattice perspective. Of particular interest is the variation of I_GDH(Q²) with Q², and what it may teach us about the origin and magnitude of higher-twist contributions.

An explicit evaluation of the spin asymmetry of the deuteron and the associated GDH sum rule is presented which includes disintegration, single and double pion and eta production. For the GDH integral a large cancellation is found between the disintegration channel and the meson production channels. Furthermore, first results for the contribution of the disintegration channel to the generalized GDH integral at constant four-momentum transfer reveal a dominance of the isovector M1 transition to the ¹S₀-state near threshold resulting in a negative contribution with a minimum around Q² ≈ 0.2 fm⁻² which is driven by the nucleon anomalous isovector magnetic moment.

The Burkhardt-Cottingham, Bjorken and generalized GDH sum rules are all consequences of the Q²-dependent dispersion relations for the virtual photon Compton amplitudes. These integrals are investigated for a ³He target at low Q².

An approach for the description of the final state interaction in the evaluation of inclusive electromagnetic responses of a polarized ³He target, is briefly illustrated. Preliminary results of calculations, where the final state interaction is fully taken into account for the two-body break-up channel, are compared with experimental data, showing a very encouraging improvement with respect to the plane wave impulse approximation results.

Nuclear weapons are unique in their terrifying potential. With an energy release a million times larger than that of previous explosives, mass destruction is inevitable. The prospect of the spread of nuclear weapons and other dangerous technologies into the hands of suicidal terrorists and rogue nations unrestrained by the norms of civilized behavior has led President Bush to remark that “the gravest danger our nation faces lies at the crossroads of radicalism and technology.” This talk will address what can and should be done, in the face of new challenges in times punctuated by terrorist threats, to sustain and strengthen the non-proliferation regime, taking into consideration technical realities, and the roles and limits of diplomatic initiatives and of military force.

AUTHOR INDEX

PROGRAM OF THE SYMPOSIUM

LIST OF PARTICIPANTS