2006/11/28 by Stanley J. Brodsky, S. J. Brodsky, D. Chakrabarti +6 · 60 citations
Physics and Astronomy · #Amplitude #Compton scattering #Coordinate space #Fourier transform #Geometry #Hadron #High-Energy Particle Collisions Research #Invariant (physics) #Invariant mass #Particle physics #Particle physics theoretical and experimental studies #Parton #Physics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Scattering #Scattering amplitude #Wave function #hep-ph
paper · pdf · doi:10.1103/physrevd.75.014003
published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 75(1) (American Physical Society) · minor modification to text, preprint number updated
arxiv created 2006/11/28 · openalex publication_date 2007/01/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The Fourier transform of the deeply virtual Compton scattering amplitude (DVCS) with respect to the skewness parameter \ensuremathζ=Q2/2p\ifmmode⋅\else\textperiodcentered\fiq can be used to provide an image of the target hadron in the boost-invariant variable \ensuremathσ, the coordinate conjugate to light-front time \ensuremathτ=t+z/c. As an illustration, we construct a consistent covariant model of the DVCS amplitude and its associated generalized parton distributions using the quantum fluctuations of a fermion state at one loop in QED, thus providing a representation of the light-front wave functions (LFWFs) of a lepton in \ensuremathσ space. A consistent model for hadronic amplitudes can then be obtained by differentiating the light-front wave functions with respect to the bound-state mass. The resulting DVCS helicity amplitudes are evaluated as a function of \ensuremathσ and the impact parameter \stackrel\ensuremath→b_\ensuremath⊥, thus providing a light-front image of the target hadron in a frame-independent three-dimensional light-front coordinate space. Models for the LFWFs of hadrons in (3+1) dimensions displaying confinement at large distances and conformal symmetry at short distances have been obtained using the AdS/CFT method. We also compute the LFWFs in this model in invariant three-dimensional coordinate space. We find that, in the models studied, the Fourier transform of the DVCS amplitudes exhibit diffraction patterns. The results are analogous to the diffractive scattering of a wave in optics where the distribution in \ensuremathσ measures the physical size of the scattering center in a one-dimensional system.