Nucleon Compton scattering in the Dyson-Schwinger approach
arXiv:1212.1761 · doi:10.1103/PhysRevD.87.036006
Abstract
We analyze the nucleon's Compton scattering amplitude in the Dyson-Schwinger/Faddeev approach. We calculate a subset of diagrams that implements the nonperturbative handbag contribution as well as all t-channel resonances. At the quark level, these ingredients are represented by the quark Compton vertex whose analytic properties we study in detail. We derive a general form for a fermion two-photon vertex that is consistent with its Ward-Takahashi identities and free of kinematic singularities, and we relate its transverse part to the onshell nucleon Compton amplitude. We solve an inhomogeneous Bethe-Salpeter equation for the quark Compton vertex in rainbow-ladder truncation and implement it in the nucleon Compton scattering amplitude. The remaining ingredients are the dressed quark propagator and the nucleon's bound-state amplitude which are consistently solved from Dyson-Schwinger and covariant Faddeev equations. We verify numerically that the resulting quark Compton vertex and nucleon Compton amplitude both reproduce the pion-photon transition form factor when the pion pole in the t-channel is approached.
36 pages, 10 figures, 5 tables
References in corpus (57)
- The Infrared Behavior of QCD Green's Functions - Confinement, Dynamical Symmetry Breaking, and Hadrons as Relativistic Bound States
- pi- and K-meson Bethe-Salpeter Amplitudes
- Infrared Properties of QCD from Dyson-Schwinger equations
- Bethe-Salpeter Study of Vector Meson Masses and Decay Constants
- Pion mass and decay constant
- Theory of deeply virtual Compton scattering on the nucleon
- Collective perspective on advances in Dyson-Schwinger Equation QCD
- Sketching the Bethe-Salpeter kernel
- Dispersion relations in real and virtual Compton scattering
- Effective theory of the Delta(1232) in Compton scattering off the nucleon
- Dressed-quark anomalous magnetic moments
- Nucleon mass from a covariant three-quark Faddeev equation
- The quark-gluon vertex in Landau gauge QCD: Its role in dynamical chiral symmetry breaking and quark confinement
- Review of two-photon exchange in electron scattering
- Electromagnetic Form Factors of the Nucleon and Compton Scattering
- Aspects of Hadron Physics
- Gauge-invariant theory of pion photoproduction with dressed hadrons
- Probing the gluon self-interaction in light mesons
- Virtual Compton Scattering and Generalized Polarizabilities of the Proton
- Using effective field theory to analyse low-energy Compton scattering data from protons and light nuclei
- Nucleon electromagnetic form factors from the covariant Faddeev equation
- Proton polarisability contribution to the Lamb shift in muonic hydrogen at fourth order in chiral perturbation theory
- Consistent Calculation of the Nucleon Electromagnetic Polarizabilities in Chiral Perturbation Theory Beyond Next-to-Leading Order
- Electromagnetic Transition Form Factors of Light Mesons
- Probing Unquenching Effects in the Gluon Polarisation in Light Mesons
- Compton Scattering and the Spin Structure of the Nucleon at Low Energies
- Beyond the rainbow: effects from pion back-coupling
- Hadronic unquenching effects in the quark propagator
- Polarizability of the Nucleon and Compton Scattering
- The Electromagnetic Self-Energy Contribution to M_p - M_n and the Isovector Nucleon Magnetic Polarizability
- Structure analysis of the virtual Compton scattering amplitude at low energies
- Extracting Nucleon Magnetic Moments and Electric Polarizabilities from Lattice QCD in Background Electric Fields
- Quark-gluon vertex from lattice QCD
- Nucleon axial and pseudoscalar form factors from the covariant Faddeev equation
- On Nucleon Electromagnetic Form Factors
- Dispersion relation formalism for virtual Compton scattering off the proton
- Delta and Omega masses in a three-quark covariant Faddeev approach
- Compton scattering on the proton, neutron, and deuteron in chiral perturbation theory to O(Q^4)
- Generalized polarizabilities and the spin-averaged amplitude in virtual Compton scattering off the nucleon
- Gauging of equations method. I. Electromagnetic currents of three distinguishable particles
- Nucleon to Delta electromagnetic transition in the Dyson-Schwinger approach
- Virtual Compton scattering off the nucleon at low energies
- Natural Resolution of the Proton Size Puzzle
- Hadron structure at low Q^2
- Gauging of equations method. II. Electromagnetic currents of three identical particles
- Compton scattering from chiral dynamics with unitarity and causality
- Hadronic decays of mesons and baryons in the Dyson-Schwinger approach
- Low-energy and low-momentum representation of the virtual Compton scattering amplitude
- Unified description of hadron-photon and hadron-meson scattering in the Dyson-Schwinger approach
- Meson-Baryon-Baryon Vertex Function and the Ward-Takahashi Identity
- Nucleon polarizabilities in the perturbative chiral quark model
- Covariant solution of the three-quark problem in quantum field theory: the nucleon
- Real and Virtual Compton Scattering: the nucleon polarisabilities
- Electromagnetic Polarizabilities and Charge Radii of the Nucleons in the Diquark-model
- New approach to low energy Virtual Compton Scattering and generalized polarizabilities of the nucleon
- On the Compton scattering vertex for massive scalar QED
- Nucleon Polarizabilities: Theory
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- QCD and strongly coupled gauge theories: challenges and perspectives
- Baryons as relativistic three-quark bound states
- Insights into the Emergence of Mass from Studies of Pion and Kaon Structure
- The three-gluon vertex in Landau gauge
- The anomalous magnetic moment of the muon in the Standard Model: an update
- Symmetry, symmetry breaking, and pion parton distributions
- Effects of divergent ghost loops on the Green's functions of QCD
- Nucleon Polarizabilities: from Compton Scattering to Hydrogen Atom
- The quark-gluon vertex in Landau gauge bound-state studies
- Spectra of heavy quarkonia in a Bethe-Salpeter-equation approach
- Four-point functions and the permutation group S4
- Single pseudoscalar meson pole and pion box contributions to the anomalous magnetic moment of the muon
- Contact-interaction Faddeev equation and, inter alia, proton tensor charges
- Confinement, quark mass functions, and spontaneous chiral symmetry breaking in Minkowski space
- On the large-Q^2 behavior of the pion transition form factor
- Jülich-Bonn-Washington Model for Pion Electroproduction Multipoles
- Nucleon resonances in Compton scattering
- Probing the tensor structure of lattice three-gluon vertex in Landau gauge
- Generalised parton distributions from the off-forward Compton amplitude in lattice QCD
- First look at heavy-light mesons with a dressed quark-gluon vertex
- Quark scalar, axial, and pseudoscalar charges in the Schwinger-Dyson formalism
- Coupled-channel analysis of pion- and eta-electroproduction with the Jülich-Bonn-Washington model
- Generalized polarizabilities of the nucleon in baryon chiral perturbation theory
- Light-quarkonium spectra and orbital-angular-momentum decomposition in a Bethe-Salpeter-equation approach
- Timelike form factor for the anomalous process
- Looking at QED with Dyson-Schwinger equations: basic equations, Ward-Takahashi identities and the two-photon-two-fermion irreducible vertex
- Gauge invariant formulation of 3 decay of particle-antiparticle bound states
- Getting a handle on correlation functions
- Nucleon Compton scattering from the Dyson-Schwinger perspective