Combining Lattice QCD Results with Regge Phenomenology in a Description of Quark Distribution Functions

The most striking feature of quark distribution functions transformed to the longitudinal distance representation is the recognizable separation of small and large longitudinal distances. While the former are responsible for the average properties of parton distributions, the latter can be shown to determine specifically their small-$x$ behavior. In this paper we demonstrate how the distribution at intermediate longitudinal distances can be approximated by taking into account constraints which follow from the general properties of parton densities, such as their support and behavior at $x \to 1$. We show that the combined description of small, intermediate, and large longitudinal distances allows a good approximation of both shape and magnitude of parton distribution functions. As an application we have calculated low-virtuality C even and odd (valence) u and d quark parton densities of the nucleon and the C-even transversity distribution $h_1(x)$, combining recent QCD sum rules and lattice QCD results with phenomenological information about their small-$x$ behavior.