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Title: Hadron optics in three-dimensional invariant coordinate space from deeply virtual Compton scattering

Abstract

The Fourier transform of the deeply virtual Compton scattering amplitude (DVCS) with respect to the skewness parameter {zeta}=Q{sup 2}/2p{center_dot}q can be used to provide an image of the target hadron in the boost-invariant variable {sigma}, the coordinate conjugate to light-front time {tau}=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 {sigma} 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 {sigma} and the impact parameter b-vector{sub perpendicular}, 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 amplitudesmore » exhibit diffraction patterns. The results are analogous to the diffractive scattering of a wave in optics where the distribution in {sigma} measures the physical size of the scattering center in a one-dimensional system.« less

Authors:
 [1];  [2];  [3];  [4];  [1];  [5];  [5]
  1. Stanford Linear Accelerator Center, Stanford University, Stanford, California 94309 (United States)
  2. Department of Physics, University of Florida, Gainesville, Florida-32611-8440 (United States)
  3. Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700064 (India)
  4. Department of Physics, Indian Institute of Technology, Powai, Mumbai 400076 (India)
  5. (United States)
Publication Date:
OSTI Identifier:
20933218
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 1; Other Information: DOI: 10.1103/PhysRevD.75.014003; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ASYMMETRY; BEAM OPTICS; BOUND STATE; COMPTON EFFECT; CONFORMAL INVARIANCE; DIFFRACTION; FOURIER TRANSFORMATION; HADRONS; HELICITY; IMPACT PARAMETER; LEPTONS; MATHEMATICAL SPACE; QUANTUM ELECTRODYNAMICS; THREE-DIMENSIONAL CALCULATIONS; WAVE FUNCTIONS

Citation Formats

Brodsky, S. J., Chakrabarti, D., Harindranath, A., Mukherjee, A., Vary, J. P., Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, and Lawrence Livermore National Laboratory, L-414, 7000 East Avenue, Livermore, California, 94551. Hadron optics in three-dimensional invariant coordinate space from deeply virtual Compton scattering. United States: N. p., 2007. Web. doi:10.1103/PHYSREVD.75.014003.
Brodsky, S. J., Chakrabarti, D., Harindranath, A., Mukherjee, A., Vary, J. P., Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, & Lawrence Livermore National Laboratory, L-414, 7000 East Avenue, Livermore, California, 94551. Hadron optics in three-dimensional invariant coordinate space from deeply virtual Compton scattering. United States. doi:10.1103/PHYSREVD.75.014003.
Brodsky, S. J., Chakrabarti, D., Harindranath, A., Mukherjee, A., Vary, J. P., Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, and Lawrence Livermore National Laboratory, L-414, 7000 East Avenue, Livermore, California, 94551. Mon . "Hadron optics in three-dimensional invariant coordinate space from deeply virtual Compton scattering". United States. doi:10.1103/PHYSREVD.75.014003.
@article{osti_20933218,
title = {Hadron optics in three-dimensional invariant coordinate space from deeply virtual Compton scattering},
author = {Brodsky, S. J. and Chakrabarti, D. and Harindranath, A. and Mukherjee, A. and Vary, J. P. and Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011 and Lawrence Livermore National Laboratory, L-414, 7000 East Avenue, Livermore, California, 94551},
abstractNote = {The Fourier transform of the deeply virtual Compton scattering amplitude (DVCS) with respect to the skewness parameter {zeta}=Q{sup 2}/2p{center_dot}q can be used to provide an image of the target hadron in the boost-invariant variable {sigma}, the coordinate conjugate to light-front time {tau}=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 {sigma} 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 {sigma} and the impact parameter b-vector{sub perpendicular}, 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 {sigma} measures the physical size of the scattering center in a one-dimensional system.},
doi = {10.1103/PHYSREVD.75.014003},
journal = {Physical Review. D, Particles Fields},
number = 1,
volume = 75,
place = {United States},
year = {Mon Jan 01 00:00:00 EST 2007},
month = {Mon Jan 01 00:00:00 EST 2007}
}
  • The Fourier transform of the deeply virtual Compton scattering amplitude (DVCS) with respect to the skewness parameter {zeta} = Q{sup 2}/2p {center_dot} q can be used to provide an image of the target hadron in the boost-invariant variable {sigma}, the coordinate conjugate to light-front time {tau} = 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 wavefunctions of a lepton in {sigma} space. A consistent model formore » hadronic amplitudes can then be obtained by differentiating the light-front wavefunctions with respect to the bound-state mass. The resulting DVCS helicity amplitudes are evaluated as a function of {sigma} and the impact parameter {rvec b}{sub {perpendicular}}, thus providing a light-front ''photograph'' of the target hadron in a frame-independent three-dimensional light-front 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 {sigma} measures the physical size of the scattering center in a one-dimensional system.« less
  • The Fourier transform of the deeply virtual Compton scattering amplitude (DVCS) with respect to the skewness parameter {zeta} = Q{sup 2}/2p {center_dot} q can be used to provide an image of the target hadron in the boost-invariant variable {sigma}, the coordinate conjugate to light-front time {tau} = 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 of a lepton in {sigma} space. A consistent modelmore » 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 {sigma} and the impact parameter {rvec b}{sub {perpendicular}}, 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 ? measures the physical size of the scattering center in a one-dimensional system.« less
  • We show that the Fourier transform of the Deeply Virtual Compton Scattering (DVCS) amplitude with respect to the skewness variable {zeta} provides a unique way to visualize the light-front wavefunctions (LFWFs) of the target state in the boost-invariant longitudinal coordinate space variable ({sigma} = P{sup +}y{sup -}/2). The results are analogous to the diffractive scattering of a wave in optics in which the dependence of the amplitude on {sigma} measures the physical size of the scattering center of a one-dimensional system. If one combines this longitudinal transform with the Fourier transform of the DVCS amplitude with respect to the transversemore » momentum transfer {Delta}{sup {perpendicular}}, one can obtain a complete three-dimensional description of hadron optics at fixed light-front time {tau} = t + z/c. 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{sup 2} and study the corresponding DVCS amplitudes in {sigma} space.« less
  • In the framework of generalized parton distributions, we study the helicity-dependent and independent cross sections measured in Hall A and the beam spin asymmetries measured in Hall B at Jefferson Laboratory. We perform a global fit of these data and fits on each kinematic bin. We extract the real and imaginary parts of the Compton form factor H under the main hypothesis of dominance of the generalized parton distribution H and twist 2 accuracy. We discuss our results and compare to previous extractions as well as to the VGG model. We pay extra attention to the estimation of errors onmore » the extraction of H.« less
  • We use gauge/gravity duality to study deeply virtual Compton scattering (DVCS) in the limit of high center of mass energy at fixed momentum transfer, corresponding to the limit of low Bjorken x, where the process is dominated by the exchange of the pomeron. At strong coupling, the pomeron is described as the graviton Regge trajectory in AdS space, with a hard wall to mimic confinement effects. This model agrees with HERA data in a large kinematical range. The behavior of the DVCS cross section for very high energies, inside saturation, can be explained by a simple AdS black disk model.more » In a restricted kinematical window, this model agrees with HERA data as well.« less