Matthias Burkardt

IMPACT PARAMETER SPACE INTERPRETATION FOR GENERALIZED PARTON DISTRIBUTIONS

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 impact parameter distribution of unpolarized quarks for an unpolarized nucleon,

Light front quantization

\tilde{H}

Impact parameter dependent parton distributions and transverse single spin asymmetries

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.

Transverse deformation of parton distributions and transversity decomposition of angular momentum

More than twenty years after quantum chromodynamics (QCD) was introduced as a microscopic theory of strong interactions, very little is known about its solutions. At least in principle, it should be possible to describe the interaction of nucleons with external probes using quark and gluon degrees of freedom on the basis of QCD. So far, however, the extreme complexity of this theory has slowed any progress in this direction considerably. To investigate QCD further this paper investigates the following topics: Canonical Quantization; The Light-Front Vacuum; Perturbative Renormalization; and Nonperturbative Calculations.

Sivers asymmetry and generalized parton distributions in impact parameter space

Generalized parton distributions (GPDs) with purely transverse momentum transfer can be interpreted as Fourier transforms of the distribution of partons in impact parameter space. The helicity-flip GPD

Chromodynamic lensing and transverse single spin asymmetries

E(x,0,-\Dps)

Parton orbital angular momentum and final state interactions

is related to the distortion of parton distribution functions in impact parameter space if the target is not a helicity eigenstate, but has some transverse polarization. This transverse distortion can be used to develop an intuitive explanation for various transverse single spin asymmetries.

The relativistic bound state problem in QCD: transverse lattice methods

Impact parameter dependent parton distributions are transversely distorted when one considers transversely polarized nucleons and/or quarks. This provides a physical mechanism for the

Generalized parton distributions for large x

T

Are all Boer–Mulders functions alike?

-odd Sivers effect in semi-inclusive deep-inelastic scattering. The transverse distortion can also be connected with Jis quark angular momentum relation. The distortion of chirally odd impact parameter dependent parton distributions is related to chirally odd generalized parton distributions (GPDs). This result is used to provide a decomposition of the quark angular momentum with respect to (w.r.t.) quarks of definite transversity. Chirally odd GPDs can thus be used to determine the correlation between quark spin and quark angular momentum in unpolarized nucleons. Based on the transverse distortion, we also suggest a qualitative connection between chirally odd GPDs and the Boer-Mulders effect.