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

References in corpus (6)

• Analysis of Pion Photoproduction Data
• The Q^2 evolution of the generalized Gerasimov-Drell-Hearn integral for the neutron using a He-3 target
• Burkhardt-Cottingham sum rule and forward spin polarizabilities in Heavy Baryon Chiral Perturbation Theory
• The $Q^2$-dependence of the generalised Gerasimov-Drell-Hearn integral for the deuteron, proton and neutron
• Generalized spin polarizabilities of the nucleon in Heavy Baryon Chiral Perturbation Theory at order $\mathcal{O}(p^4)$
• Virtual Compton Scattering

Cited by in corpus (166)

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• Electromagnetic excitation of the Delta(1232)-resonance
• Generalized Parton Distributions in the valence region from Deeply Virtual Compton Scattering
• The Spin Structure of the Proton
• Electromagnetic Form Factors of the Nucleon and Compton Scattering
• Two-Photon Physics in Hadronic Processes
• Using effective field theory to analyse low-energy Compton scattering data from protons and light nuclei
• Roy-Steiner equations for gamma gamma -> pi pi
• Higher order proton structure corrections to the Lamb shift in muonic hydrogen
• The Spin Structure of the Nucleon
• Predictive powers of chiral perturbation theory in Compton scattering off protons
• Nucleon Polarizabilities: from Compton Scattering to Hydrogen Atom
• Compton scattering from the proton in an effective field theory with explicit Delta degrees of freedom
• Chiral perturbation theory of muonic hydrogen Lamb shift: polarizability contribution
• Dispersion relations and subtractions in hard exclusive processes
• Dispersive evaluation of the D-term form factor in deeply virtual Compton scattering
• Experimental study of isovector spin sum rules
• Signatures of Chiral Dynamics in Low Energy Compton Scattering off the Nucleon
• Resonance estimates for single spin asymmetries in elastic electron-nucleon scattering
• The Present and Future of QCD
• New insights into the spin structure of the nucleon
• Four-point functions and the permutation group S4
• Proton structure corrections to electronic and muonic hydrogen hyperfine splitting
• Compton scattering on the proton, neutron, and deuteron in chiral perturbation theory to O(Q^4)
• Forward virtual Compton scattering and the Lamb shift in chiral perturbation theory
• Moments of the Spin Structure Functions g_1^p and g_1^d for 0.05 < Q^2 < 3.0 GeV^2
• Proton polarizability effect in the Lamb shift of the hydrogen atom
• Novel approaches in Hadron Spectroscopy
• Gold-plated moments of nucleon structure functions in baryon chiral perturbation theory
• Two-photon exchange correction in elastic unpolarized electron-proton scattering at small momentum transfer
• Proton spin polarizabilities from polarized Compton scattering
• Measurement of the Generalized Forward Spin Polarizabilities of the Neutron
• Hadron structure at low Q^2
• Dispersion relation analysis of the radiative corrections to $g_A$ in the neutron $\beta$-decay
• The Gerasimov-Drell-Hearn Sum Rule and the Spin Structure of the Nucleon
• Lattice QCD evaluation of the Compton amplitude employing the Feynman-Hellmann theorem
• Measurements of Double-Polarized Compton Scattering Asymmetries and Extraction of the Proton Spin Polarizabilities
• Hadron Polarizabilities
• Predictions of covariant chiral perturbation theory for nucleon polarisabilities and polarised Compton scattering
• Measurements of the Generalized Electric and Magnetic Polarizabilities of the Proton at Low Q2 Using the VCS Reaction
• Compton scattering from chiral dynamics with unitarity and causality
• Nucleon Compton scattering in the Dyson-Schwinger approach
• Sum Rules for Magnetic Moments and Polarizabilities in QED and Chiral Effective-Field Theory
• Sum Rules and Moments of the Nucleon Spin Structure Functions
• Nucleon resonance contributions to unpolarised inclusive electron scattering
• Dispersion Theory in Electromagnetic Interactions
• Two-photon exchange correction to the hyperfine splitting in muonic hydrogen
• Quantum field theory for spin operator of the photon
• Measurement of the Q^2 Dependence of the Deuteron Spin Structure Function g_1 and its Moments at Low Q^2 with CLAS
• Proton polarisabilities from Compton data using Covariant Chiral EFT
• Evaluation of the forward Compton scattering off protons: I. Spin-independent amplitude
• Light-front interpretation of Proton Generalized Polarizabilities
• Model-independent effects of Delta excitation in nucleon polarizabilities
• A new measurement of the structure functions $P_{LL}-P_{TT}/epsilon$ and $P_{LT}$ in virtual Compton scattering at $Q^2=$ 0.33 (GeV/c)${}^2$
• Higher order forward spin polarizability
• Forward two-photon exchange in elastic lepton-proton scattering and hyperfine-splitting correction
• Nucleon resonances in Compton scattering
• Q-ball dynamics from atomic Bose-Einstein condensates
• Generalised parton distributions from the off-forward Compton amplitude in lattice QCD
• Forward doubly-virtual Compton scattering off the nucleon in chiral perturbation theory: II. Spin polarizabilities and moments of polarized structure functions
• Spin Polarizabilities of the Nucleon from Polarized Low Energy Compton Scattering
• The polarizability of the pion: no conflict between dispersion theory and chiral perturbation theory
• Measurement of the proton spin structure at long distances
• 3He Spin-Dependent Cross Sections and Sum Rules
• Unified description of hadron-photon and hadron-meson scattering in the Dyson-Schwinger approach
• Dispersive evaluation of the Lamb shift in muonic deuterium from chiral effective field theory
• Measurement of the 3He Spin-Structure Functions and of Neutron (3He) Spin-Dependent Sum Rules at 0.035<Q^2<0.24 GeV^2
• CMB circular and B-mode polarization from new interactions
• Explicit Delta(1232) Degrees of Freedom in Compton Scattering off the Deuteron
• New experimental constraints on polarizability corrections to hydrogen hyperfine structure
• Virtual Compton Scattering and the Generalized Polarizabilities of the Proton at Q^2=0.92 and 1.76 GeV^2
• Moments of Spin Structure Functions: Sum Rules and Polarizabilities
• New Predictions for generalized spin polarizabilities from heavy baryon chiral perturbation theory
• Generalized polarizabilities of the nucleon in baryon chiral perturbation theory
• Proton scalar dipole polarizabilities from real Compton scattering data, using fixed-t subtracted dispersion relations and the bootstrap method
• Gamma decay of the ${}^{154}$Sm Isovector Giant Dipole Resonance: Smekal-Raman Scattering as a Novel Probe of Nuclear Ground-State Deformation
• Compton Scattering from the Deuteron below Pion-Production Threshold
• Electromagnetic polarizabilities of the nucleon and properties of the $\sigma$-meson pole contribution
• The MAID Legacy and Future
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• Electroexcitation of the ${\Delta }^{+}(1232)$ at low momentum transfer
• First extraction of the scalar proton dynamical polarizabilities from real Compton scattering data
• Nucleon polarizabilities in the perturbative chiral quark model
• The Standard Model theory of neutron beta decay
• Resonant contributions to inclusive nucleon structure functions from exclusive meson electroproduction data
• Separation of proton polarizabilities with the beam asymmetry of Compton scattering
• Beam-helicity asymmetry in photon and pion electroproduction in the Delta(1232) resonance region at Q^2= 0.35 (GeV/c)^2
• Virtual Compton Scattering measurements in the ${\gamma }^{\ast }N\to \Delta$ transition
• Octet Baryons in Large Magnetic Fields
• Analyzing the Effects of Neutron Polarizabilities in Elastic Compton Scattering off ${}^3$He
• Measured proton electromagnetic structure deviates from theoretical predictions
• Higher moments of nucleon spin structure functions in heavy baryon chiral perturbation theory and in a resonance model
• Evaluation of the forward Compton scattering off protons: II. Spin-dependent amplitude and observables
• Target-normal single-spin asymmetry in elastic electron-nucleon scattering
• Real and Virtual Compton Scattering: the nucleon polarisabilities
• What different variants of chiral EFT predict for the proton Compton differential cross section - and why
• Dispersion Theory and the Low Energy Constants for Neutral Pion Photoproduction
• Forward doubly-virtual Compton scattering off the nucleon in chiral perturbation theory: the subtraction function and moments of unpolarized structure functions
• Spin polarizabilities of the proton by measurement of Compton double-polarization observables
• Virtual Compton Scattering measurements in the nucleon resonance region
• Virtual Compton Scattering and Nucleon Generalized Polarizabilities
• Electromagnetic polarizabilities and the excited states of the nucleon
• Spin-dependent sum rules connecting real and virtual Compton scattering verified
• Compton Scattering off Pions and Electromagnetic Polarizabilities
• Quantum field theoretical framework for the electromagnetic response of graphene and dispersion relations with implications to the Casimir effect
• Dispersion theory of nucleon Compton scattering and polarizabilities
• Partial-wave analysis of proton Compton scattering data below the pion-production threshold
• New Insight in the $Q^2$-Dependence of Proton Generalized Polarizabilities
• Comprehensive Study of Observables in Compton Scattering on the Nucleon
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• Q^2 Evolution of Generalized Baldin Sum Rule for the Proton
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• Polarizabilities of the nucleon and spin dependent photo-absorption
• $\Delta (1232)$-Resonance in the Hydrogen Spectrum
• Chiral perturbation theory - Success and challenge
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• Single spin asymmetries in elastic electron-nucleon scattering
• Hyperon forward spin polarizability gamma0 in baryon chiral perturbation theory
• Two-current transition amplitudes with two-body final states
• New Evaluation of Proton Structure Corrections to Hydrogen Hyperfine Splitting
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• Resonant contributions to polarized proton structure functions
• Moments and power corrections of longitudinal and transverse proton structure functions from lattice QCD
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• Hadron Structure in Lattice QCD
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• Measurement of the Generalized Polarizabilities of the Proton at Intermediate $Q^2$
• A new Monte Carlo-based fitting method
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• Hadron Structure in Chiral Perturbation Theory
• Nucleon Polarisabilities from Compton Scattering off the One- and Few-Nucleon System
• Highlights and Perspectives of the JLab Spin Physics Program
• Forward doubly-virtual Compton scattering off an unpolarised deuteron in pionless effective field theory
• Compton scattering in TFD formalism
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• Nucleon Polarizabilities: Theory
• Virtual Compton scattering at low energies with a positron beam
• Low energy theorem for virtual Compton scattering and generalized sum rules of the nucleon
• Hadronic deuteron polarizability contribution to the Lamb shift in muonic deuterium
• Hyperon forward spin polarizabilty gamma0
• Superconvergence Relations and Parity Violating analogue of GDH sum rule
• Nucleon Spin-Polarisabilities from Polarisation Observables in Low-Energy Deuteron Compton Scattering
• Chiral effective field theories of the strong interactions
• Towards a microscopic understanding of nucleon polarizabilities
• Measurement of the nucleon spin structure functions for 0.01<$Q^2$<1 GeV${}^2$ using CLAS
• Soft-photon radiative corrections to the $e^{-}p\to e^{-}p{l}^{-}{l}^{+}$ process
• Lattice QCD calculation of the Compton amplitude subtraction function
• Electron Beam Single-Spin Asymmetries in the Resonance Region with Final Hadrons Observed
• Compton Scattering by the Nucleon
• Charge and spin asymmetries in elastic lepton-nucleon scattering
• Dispersion theory of nucleon polarizabilities and outlook on chiral effective field theory
• Compton Scattering from the Deuteron above Pion-Production Threshold
• Generalized sum rules of the nucleon in the CQM
• The Proton Electromagnetic Generalized Polarizabilities
• Energy of a point-like neutron in an external electromagnetic field
• Getting a handle on correlation functions
• Resonance Structure and Polarizability of the nucleon
• Two-photon physics
• Proton Structure Corrections to Hydrogen Hyperfine Splitting
• Predictions of chiral perturbation theory for Compton scattering off protons
• A reassessment of nuclear effects in muonic deuterium using pionless effective field theory at N3LO