# 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 »

- Authors:

- Stanford Linear Accelerator Center, Stanford University, Stanford, California 94309 (United States)
- Department of Physics, University of Florida, Gainesville, Florida-32611-8440 (United States)
- Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700064 (India)
- Department of Physics, Indian Institute of Technology, Powai, Mumbai 400076 (India)
- (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}

}