Impact Parameter Space Interpretation for Generalized Parton Distributions

Abstract

The Fourier transform of generalized parton distribution functions at ξ = 0 describes the distribution of partons in the transverse plane. The physical significance of these impact parameter dependent parton distribution functions is discussed. In particular, it is shown that they satisfy positivity constraints which justify their physical interpretation as a probability density. The generalized parton distribution H is related to the impact parameter distribution of unpolarized quarks for an unpolarized nucleon,H is related to the distribution of longitudinally polarized quarks in a longitudinally polarized nucleon, and E is related to the distortion of the unpolarized quark distribution in the transverse plane when the nucleon has transverse polarization. The magnitude of the resulting transverse flavor dipole moment can be related to the anomalous magnetic moment for that flavor in a model independent way.

Chromodynamic lensing and transverse single spin asymmetries

“…This interpretation becomes even more transparent after switching to an impact parameter representation [8,9,10,11] …”

“…If the target is polarized in the x-direction in the infinite momentum frame, the unpolarized impact parameter dependent PDFs for flavor q reads [11] …”

Generalized parton distributions and structure functions from full lattice QCD

“…In the limit where the momentum transfer ∆ to the nucleon is purely transverse, i.e. ∆ = (0, ∆ ⊥ ) and ξ = 0, GPDs regain a probabilistic interpretation [4]. In the 2 forward limit (∆ = 0), these distributions reduce to the Feynman parton distributions.…”

“…Generalized parton distributions (GPDs) [1,2] describe the coherence of two different hadron wave functions ψ † (x + ξ/2) ψ(x − ξ/2), one where the parton carries fractional momentum x + ξ/2 and one where this fraction is x − ξ/2, from which further information on the transverse distribution of partons can be drawn [3,4]. In the limit where the momentum transfer ∆ to the nucleon is purely transverse, i.e.…”

A Measurement of the neutron electric form factor at very large momentum transfer using polaried electrions scattering from a polarized helium-3 target

“…Recent calculations using the GPD's have provided insight into the transverse distribution of partons within the nucleon [62,2]. GPDs using form factor input have also provided new methods of calculating the charge distributions of nucleons [63,64,65] without resorting to the Breit frame transformations.…”