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The third moment d2 of the twist-3 part of the nucleon spin structure function g2 is generalized to arbitrary momentum transfer Q2 and is evaluated in heavy baryon chiral perturbation theory (HBChPT) up to order [Omicron](p4) and in a unitary isobar model (MAID). We show how to link d2 as well as higher moments of the nucleon spin structure functions g1 and g2 to nucleon spin polarizabilities. We compare our results with the most recent experimental data, and find a good description of these available data within the unitary isobar model. We proceed to extract the twist-4 matrix element f2 which appears in the 1/Q2 suppressed term in the twist expansion of the spin structure function g1 for proton and neutron.
Recent precision spin structure data from Jefferson Lab have significantly advanced our knowledge of nucleon structure in the valence quark (high-x) region and improved our understanding of higher-twist effects, spin sum rules and quark-hadron duality. First, results of a precision measurement of the neutron spin asymmetry, A[sub 1][sup n], in the high-x region are discussed. The new data shows clearly, for the first time, that A[sub 1][sup n] becomes positive at high x. They provide crucial input for the global fits to world data to extract polarized parton distribution functions. Preliminary results on A[sub 1][sup p] and A[sub 1][sup d] in the high-x region have also become available. The up and down quark spin distributions in the nucleon were extracted. The results for [Delta]d/d disagree with the leading-order pQCD prediction assuming hadron helicity conservation. Then, results of a precision measurement of the g[sub 2][sup n] structure function to study higher-twist effects are presented. The data show a clear deviation from the lead-twist contribution, indicating a significant higher-twist (twist-3 or higher) effect. The second moment of the spin structure functions and the twist-3 matrix element d[sub 2][sup n] results were extracted at a high Q[sup 2] of 5 GeV[sup 2] from the measured A[sub 2][sup n] in the high-x region in combination with existing world data and compared with a Lattice QCD calculation. Results for d[sub 2][sup n] at low-to-intermediate Q[sup 2] from 0.1 to 0.9 GeV[sup 2] were also extracted from the JLab data. In the same Q[sup 2] range, the Q[sup 2] dependence of the moments of the nucleon spin structure functions was measured, providing a unique bridge linking the quark-gluon picture of the nucleon and the coherent hadronic picture. Sum rules and generalized forward spin polarizabilities were extracted and compared with Chiral Perturbation Theory calculations and phenomenological models. Finally, preliminary results on the resonance spin structure functions in the Q[sup 2] range from 1 to 4 GeV[sup 2] were presented, which, in combination with DIS data, will enable a detailed study of the quark-hadron duality in spin structure functions.
The history of spin in general, and of the nucleon spin structure in particular, has been full of surprises. For the past 25 years deep inelastic lepton scattering has been studied to determine the carriers of the nucleon spin. However, it was realized only recently that a full understanding of the nucleon spin will also require detailed information on the helicity structure in the resonance region, i.e. in the realm of nonperturbative QCD.This volume gives a status report on the spin structure in the nucleon resonance region, focusing on: new experimental results from SLAC and HERMES; a first glance at the JLab experiments to map out the spin structure functions at low and intermediate four-momentum transfers; the pioneering experiment at MAMI (Mainz) to determine the Gerasimov-Drell-Hearn sum rule for real photons; and recent theoretical concepts and investigations to describe the spin structure in the frameworks of higher twist expansion, phenomenological models and chiral perturbation theory.
From its early beginnings at SLAC in the 1970's, the study of nucleon spin structure using polarized lepton beams and polarized nucleon targets has become increasingly important in nuclear and particle physics, with current experiments at several of the world's high energy and nuclear physics laboratories (CERN, DESY, SLAC and Jefferson Lab) and with enormous related theoretical studies. The understanding of the fascinating but complicated problem of nucleon spin structure has progressed substantially, but fundamental questions remain and it can be confidently predicted that future activity will be high.The Erice Course on The Spin Structure of the Nucleon covered both the experimental and theoretical aspects of the subject, and this volume includes the lectures given at the School. In many cases the lecture material has been extended and updated by the authors. In addition, several recent publications on experimental work have been added in an appendix.
The nucleon has been used as a laboratory to investigate its own spin structure and Quantum Chromodynamics. New experimental data on nucleon spin structure at low to intermediate momentum transfers combined with existing high momentum transfer data offer a comprehensive picture of the transition region from the confinement regime of the theory to its asymptotic freedom regime. Insight for some aspects of the theory is gained by exploring lower moments of spin structure functions and their corresponding sum rules (i.e. the Gerasimov-Drell-Hearn, Bjorken and Burkhardt-Cottingham). These moments are expressed in terms of an operator product expansion using quark and gluon degrees of freedom at moderately large momentum transfers. The sum rules are verified to a good accuracy assuming that no singular behavior of the structure functions is present at very high excitation energies. The higher twist contributions have been examined through the moments evolution as the momentum transfer varies from higher to lower values. Furthermore, QCD-inspired low energy effective theories, which explicitly include chiral symmetry breaking, are tested at low momentum transfers. The validity of these theories is further examined as the momentum transfer increases to moderate values. It is found that chiral perturbation calculations agree reasonably well with the first moment of the spin structure function g1 at momentum transfer of 0.1 GeV2 but fail to reproduce the neutron data in the case of the generalized polarizability [delta]{sub LT}.
This volume contains the refereed and selected contributions from the International Conference on Quark Nuclear Physics (QNP2002), held from 9 to 14 June 2002 in Jülich, Germany.
Spin structure functions of the nucleon in the region of large x and small to moderate Q2 continue to be of high current interest. The first moment of the spin structure function g1, [Gamma]1, 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. The interesting behavior in the transition region is dominated by baryon resonance excitations. We concluded an experiment to measure these observables for deuterium as part of the ''EG1'' run group in Jefferson Lab's Hall B. We used a highly polarized electron beam with energies from 1.6 GeV to 5.7 GeV and a cryogenic polarized ND3 target together with the CEBAF Large Acceptance Spectrometer (CLAS) to accumulate over 11 billion events. In this thesis, we present results for the spin structure function g1{sup d} (x, Q2), as well as its first moment, [Gamma]1{sup d}(Q2) in and above the resonance region over a Q2 range from 0.05 to 5 Gev2, based on the data taken with beam energies of 1.6 and 5.7 GeV. We also extract the behavior of A1{sup d}(x) at large x. Our data are consistent with the Hyperfine-perturbed quark model calculation which predicts that A1{sup d} (x 2!1) 2!1. We also see evidence for duality in g1{sup d} (x, Q2) at Q2> GeV2.
One of the main challenges in nuclear and particle physics in the last 20 years has been to understand how the proton''s spin is built up from its quark and gluon constituents. Quark models generally predict that about 60% of the proton''s spin should be carried by the spin of the quarks inside, whereas high energy scattering experiments have shown that the quark spin contribution is small OCo only about 30%. This result has been the underlying motivation for about 1000 theoretical papers and a global program of dedicated spin experiments at BNL, CERN, DESY and Jefferson Laboratory to map the individual quark and gluon angular momentum contributions to the proton''s spin, which are now yielding exciting results. This book gives an overview of the present status of the field: what is new in the data and what can be expected in the next few years. The emphasis is on the main physical ideas and the interpretation of spin data. The interface between QCD spin physics and the famous axial U(1) problem of QCD (eta and etaprime meson physics) is also highlighted. Sample Chapter(s). Chapter 1: Introduction (159 KB). Contents: Spin Experiments and Data; Dispersion Relations and Spin Sum Rules; g 1 Spin Sum Rules; Fixed Poles; The Axial Anomaly, Gluon topology and g (0) A; Chiral Symmetry and Axial U(1) Dynamics; QCD Inspired Models of the Proton Spin Problem; The Spin-Flavour Structure of the Proton; QCD Fits to g 1 Data; Polarized Quark Distributions; Polarized Glue o g(x, Q 2 ); Transversity; Deeply Virtual Compton Scattering and Exclusive Processes; Polarized Photon Structure Functions; Conclusions and Open Questions: How Does the Proton Spin?. Readership: Academics, as well as physicists working on particle and nuclear physics at the interface of theory and experiment.