287 research outputs found
Diffraction Patterns in Deeply Virtual Compton Scattering
We report on a calculation to 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 gives results
that 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.Comment: Presented at the 17 th International Spin Physics Symposium, Kyoto,
Japan, October 2-7, 200
Hadron Optics: Diffraction Patterns in Deeply Virtual Compton Scattering
We show that the Fourier transform of the Deeply Virtual Compton Scattering
(DVCS) amplitude with respect to the skewness variable at fixed
invariant momentum transfer squared 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 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 sharpen and the positions of the first minima move in with
increasing momentum transfer. For fixed , higher minima appear at positions
which are integral multiples of the lowest minimum. Both these observations
strongly support the analogy with diffraction in optics.Comment: Some plots modified, clarifications and references adde
Sum rules and dualities for generalized parton distributions: is there a holographic principle?
To leading order approximation, the physical content of generalized parton
distributions (GPDs) that is accessible in deep virtual electroproduction of
photons or mesons is contained in their value on the cross-over trajectory.
This trajectory separates the t-channel and s-channel dominated GPD regions.
The underlying Lorentz covariance implies correspondence between these two
regions through their relation to GPDs on the cross-over trajectory. This point
of view leads to a family of GPD sum rules which are a quark analogue of finite
energy sum rules and it guides us to a new phenomenological GPD concept. As an
example, we discuss the constraints from the JLab/Hall A data on the dominant
u-quark GPD H. The question arises whether GPDs are governed by some kind of
holographic principle.Comment: 45 pages, 4 figures, Sect. 2 reorganized for clarity. Typos in Eq.
(20) corrected. 4 new refs. Matches published versio
Generalized Parton Distributions from Hadronic Observables: Non-Zero Skewness
We propose a physically motivated parametrization for the unpolarized
generalized parton distributions, H and E, valid at both zero and non-zero
values of the skewness variable, \zeta. Our approach follows a previous
detailed study of the \zeta=0 case where H and E were determined using
constraints from simultaneous fits of the experimental data on both the nucleon
elastic form factors and the deep inelastic structure functions in the non
singlet sector. Additional constraints at \zeta \neq 0 are provided by lattice
calculations of the higher moments of generalized parton distributions. We
illustrate a method for extracting generalized parton distributions from
lattice moments based on a reconstruction using sets of orthogonal polynomials.
The inclusion in our fit of data on Deeply Virtual Compton Scattering is also
discussed. Our method provides a step towards a model independent extraction of
generalized distributions from the data. It also provides an alternative to
double distributions based phenomenological models in that we are able to
satisfy the polynomiality condition by construction, using a combination of
experimental data and lattice, without resorting to any specific mathematical
construct.Comment: 29 pages, 8 figures; added references, changed text in several place
Hadron Optics in Three-Dimensional Invariant Coordinate Space from Deeply Virtual Compton Scattering
The Fourier transform of the deeply virtual Compton scattering amplitude
(DVCS) with respect to the skewness parameter \zeta= Q^2/ 2 p.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 for
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 \vec
b_\perp, 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.Comment: minor modification to text, preprint number update
The longitudinal cross section of vector meson electroproduction
We analyze electroproduction of light vector mesons (V=rho, phi and omega) at
small Bjorken-x in the handbag approach in which the process factorizes into
general parton distributions and partonic subprocesses. The latter are
calculated in the modified perturbative approach where the transverse momenta
of the quark and antiquark forming the vector meson are retained and Sudakov
suppressions are taken into account. Modeling the generalized parton
distributions through double distributions and using simple Gaussian
wavefunctions for the vector mesons, we compute the longitudinal cross sections
at large photon virtualities. The results are in fair agreement with the
findings of recent experiments performed at HERA and HERMES.Comment: 27 pages, 20 figures, using LATEX with graphic
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