Dispersion relations in real and virtual Compton scattering

Abstract

A unified presentation is given on the use of dispersion relations in the real and virtual Compton scattering processes off the nucleon. The way in which dispersion relations for Compton scattering amplitudes establish connections between low energy nucleon structure quantities, such as polarizabilities or anomalous magnetic moments, and the nucleon excitation spectrum is reviewed. We discuss various sum rules for forward real and virtual Compton scattering, such as the Gerasimov-Drell-Hearn sum rule and its generalizations, the Burkhardt-Cottingham sum rule, as well as sum rules for forward nucleon polarizabilities, and review their experimental status. Subsequently, we address the general case of real Compton scattering (RCS). Various types of dispersion relations for RCS are presented as tools for extracting nucleon polarizabilities from the RCS data. The information on nucleon polarizabilities gained in this way is reviewed and the nucleon structure information encoded in these quantities is discussed. The dispersion relation formalism is then extended to virtual Compton scattering (VCS). The information on generalized nucleon polarizabilities extracted from recent VCS experiments is described, along with its interpretation in nucleon structure models. As a summary, the physics content of the existing data is discussed and some perspectives for future theoretical and experimental activities in this field are presented.

120 pages, 42 figures, to appear in Phys. Rep

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• Multipole analysis of pion photoproduction based on fixed t dispersion relations and unitarity
• Virtual Compton Scattering and Generalized Polarizabilities of the Proton
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• Measurement of the Proton and Deuteron Spin Structure Functions g2 and Asymmetry A2
• New empirical fits to the proton electromagnetic form factors
• The GDH Sum Rule and Related Integrals
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• Delta(1232) and the Polarizabilities of the Nucleon
• The Q^2 evolution of the generalized Gerasimov-Drell-Hearn integral for the neutron using a He-3 target
• Structure analysis of the virtual Compton scattering amplitude at low energies
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• Higher Order Polarizabilities of the Proton
• Measurement of the Total Photon Proton Cross Section and its Decomposition at 200~GeV Centre of Mass Energy
• Fixed-t subtracted dispersion relations for Compton scattering off the nucleon
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• High-Energy Forward Scattering and the Pomeron: Simple Pole versus Unitarized Models
• Dispersion relation formalism for virtual Compton scattering off the proton
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• Leading and higher twists in the proton polarized structure function at large Bjorken x
• Analytic Structure of Amplitudes in Gauge Theories with Confinement
• Generalized Polarizabilities and the Chiral Structure of the Nucleon
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• Burkhardt-Cottingham sum rule and forward spin polarizabilities in Heavy Baryon Chiral Perturbation Theory
• Generalized polarizabilities and the spin-averaged amplitude in virtual Compton scattering off the nucleon
• Deuteron Compton scattering below pion photoproduction threshold
• Virtual Compton Scattering off the Nucleon in Chiral Perturbation Theory
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• Compton scattering on the nucleon at intermediate energies and polarizabilities in a microscopic model
• First Extraction of a Spin-Polarizability of the Proton
• Virtual Compton scattering off the nucleon at low energies
• Novel analysis of chiral loop effects in the generalized Gerasimov-Drell-Hearn sum rule
• On the Extraction of the Neutron Spin Structure Functions and the Gerasimov -- Drell -- Hearn Integral from ${}^3\overrightarrow{He}(\vec{e},e^{\prime })X$ data
• Generalized dipole polarizabilities and the spatial structure of hadrons
• Elastic Compton scattering from the deuteron and nucleon polarizabilities
• Neutron polarizabilities investigated by quasi-free Compton scattering from the deuteron
• The Nucleon Spin Polarizability at Order $\mathcal{O}(p^4$) in Chiral Perturbation Theory
• Dispersion Relations and the Nucleon Polarizability
• The $Q^2$-dependence of the generalised Gerasimov-Drell-Hearn integral for the deuteron, proton and neutron
• Generalized Gerasimov-Drell-Hearn Sum Rule for the Proton-Neutron Difference in Chiral Perturbation Theory
• Compton Scattering by the Proton
• Compton Scattering by the Proton using a Large-Acceptance Arrangement
• Backward spin polarizability ${\gamma }_{\pi }$ of the proton
• The Drell-Hearn Sum Rule at Order Alpha**3
• Sum rule for the backward spin polarizability of the nucleon from a backward dispersion relation
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• The Spin and Flavour Dependence of High-Energy Photoabsorption
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• Interpolating the Nucleon's Spin-Dependent Sum Rules at High and Low Energies
• Dispersion Effects in Nucleon Polarisabilities
• Dispersion relation formalism for virtual Compton scattering and the generalized polarizabilities of the nucleon
• Real and Virtual Compton Scattering off the Nucleon
• Comment on "Complete One-Loop Analysis of the Nucleon's Spin Polarisabilities"
• The Drell-Hearn-Gerasimov Sum-Rule in QCD
• Nucleon Polarizibilities for Virtual Photons
• Generalized polarizabilities and electroexcitation of the nucleon
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