Time ordering in off-diagonal parton distributions

Abstract

We investigate the relevance of time ordering in the definition of off-diagonal parton distributions in terms of products of fields. The method we use easily allows determination of their support properties and provides a link to their interpretation from a parton point of view. It can also readily be applied to meson distribution amplitudes.}

Figures (3)

• Figure 1: Diagrams for $\gamma^\ast p \to A p$ at large $Q^2$ and small $t$, where $A$ is $(a)$ a real photon or $(b)$ a meson $M$. They consist of an off-diagonal parton distribution, a hard scattering part, and a meson distribution amplitude in case $(b)$. The partons connecting $S$ and $H$ have momenta $k$ and $k'$ with plus components $k^+ = x p^+$ and $k'^+ = x' p^+$.
• Figure 2: The two alternatives to pick up singularities in the $k^-$ plane, depending on the region of $x$. To the left (right) are the singularities above (below) the real $k^-$ axis. The diagrams show the new cut as one changes from one region of $x$ to the next, going from top to bottom on the left and from bottom to top on the right. We also give an axis in $x'$ to display the symmetry between the two partons.
• Figure 3: The two possibilities to pick up singularities in the $l^+$ plane for a meson distribution amplitude in the region $0 < y < 1$.