Generalized Parton Distributions: Proposed research 2003-

W. Detmold, G.A. Miller and B.C. Tiburzi

A project that is nearly complete is a preliminary investigation involving complex conjugate poles and parton distribution functions. There have been numerous works investigating quark propagators with complex conjugate singularities [32]. Recently solutions to the Bethe-Salpeter equation have been obtained with such a model propagator as a means to explore quark confinement [33]. Analysis of quenched lattice data for the quark propagator suggests there could be a sub-dominant pair of complex singularities [34]. Such studies are formulated in Euclidean space and naive calculation of quark distributions in Minkowski space is problematic. We have figured out how to analytically continue space-like amplitudes and thus have a means to calculate parton and generalized parton distributions using model propagators and vertices that are meromorphic functions.

There are a number of applications that should result from our work. Parton and generalized parton distributions can be calculated directly in Minkowski space for a wide class of model propagators and vertices. In particular, modeling mass functions and wave-function renormalization realistically can be achieved using meromorphic functions. Thus a Euclidean space Dyson-Schwinger type approach can be used to model and rigorously calculate light-cone dominated amplitudes in Minkowski space while maintaining full Poincaré covariance and satisfying field theoretic identities. Such models will fill a gap in existing light-cone phenomenology.

First off, we intend to model the pion and incorporate dynamical chiral symmetry breaking via the axial-vector Ward identity. We will then be able to calculate the pion form factor, quark distribution and valence distribution amplitude and finally compare with experiment. The kaon and eta mesons could also be modeled in this approach. Ultimately our goal is to model the nucleon using a non-point-like di-quark. Calculation of realistic nucleon generalized parton distributions can then be pursued. These will be essential for analyzing future measurements of deeply virtual Compton scattering by proton targets at Jefferson Lab.