Hadron Optics: Diffraction Patterns in Deeply Virtual Compton Scattering

Abstract

We show that the Fourier transform of the Deeply Virtual Compton Scattering (DVCS) amplitude with respect to the skewness variable $\zeta$ at fixed invariant momentum transfer squared $t$ provides a unique way to visualize the structure of the target hadron in the boost-invariant longitudinal coordinate space. The results are analogous to the diffractive scattering of a wave in optics. As a specific example, we utilize the quantum fluctuations of a fermion state at one loop in QED to obtain the behavior of the DVCS amplitude for electron-photon scattering. We then simulate the wavefunctions for a hadron by differentiating the above LFWFs with respect to $M^2$ and study the corresponding DVCS amplitudes in light-front longitudinal space. In both cases we observe that the diffractive patterns in the longitudinal variable conjugate to $\zeta$ sharpen and the positions of the first minima move in with increasing momentum transfer. For fixed $t$, higher minima appear at positions which are integral multiples of the lowest minimum. Both these observations strongly support the analogy with diffraction in optics.

Some plots modified, clarifications and references added

References in corpus (31)

• Gauge-Invariant Decomposition of Nucleon Spin and Its Spin-Off
• Quantum Chromodynamics and Other Field Theories on the Light Cone
• Final-State Interactions and Single-Spin Asymmetries in Semi-Inclusive Deep Inelastic Scattering
• Impact Parameter Dependent Parton Distributions and Off-Forward Parton Distributions for $\zeta \to 0$
• Impact Parameter Space Interpretation for Generalized Parton Distributions
• Hadronic Spectra and Light-Front Wavefunctions in Holographic QCD
• Quark Imaging in the Proton Via Quantum Phase-Space Distributions
• Measurement of the Beam-Spin Azimuthal Asymmetry Associated with Deeply-Virtual Compton Scattering
• Light-Cone Representation of the Spin and Orbital Angular Momentum of Relativistic Composite Systems
• Observation of exclusive DVCS in polarized electron beam asymmetry measurements
• Light-Cone Wavefunction Representation of Deeply Virtual Compton Scattering
• Femto-Photography of Protons to Nuclei with Deeply Virtual Compton Scattering
• Viewing the Proton Through "Color"-Filters
• Testing the handbag contribution to exclusive virtual Compton scattering
• The Overlap Representation of Skewed Quark and Gluon Distributions
• On Orbital Angular Momentum in Deep Inelastic Scattering
• Deeply virtual Compton scattering in next-to-leading order
• Virtual Compton Scattering Off Protons at Moderately Large Momentum Transfer
• Light-Cone Wavefunctions at Small $x$
• Deep Inelastic Structure Functions in Light-Front QCD: Radiative Corrections
• Kinks in Discrete Light Cone Quantization
• Ab initio results for the broken phase of scalar light front field theory
• Helicity-dependent Twist-two and Twist-three Generalized Parton Distributions in Light-front QCD
• Generalized Parton Distributions in the Impact Parameter Space with Non-zero Skewedness
• Impact Parameter Dependent Parton Distributions for a Composite Relativistic System
• Off-forward Matrix Elements in Light-front Hamiltonian QCD
• Transverse Spin in QCD: Radiative Corrections
• Transverse Spin in QCD and Transverse Polarized Deep Inelastic Scattering
• A transition in the spectrum of the topological sector of ${\varphi }_2^4$ theory at strong coupling
• Quark Transversity Distribution in Perturbative QCD: Light-Front Hamiltonian Approach
• Twist Four Longitudinal Structure Function in Light-Front QCD

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