Computability of GPDs near $x=\pm \xi$ in Lattice QCD

Abstract

In lattice QCD computations of generalized parton distributions (GPDs), the large momentum expansion generally requires all hard scales, $2|x\pm \xi |P^z$ and $2|1\pm x|P^z$, to be much larger than ${\Lambda }_{\mathrm{QCD}}$. We show that this condition can be relaxed for $2|x\pm \xi |P^z$ at large $\xi$, making the important $x\sim \pm \xi$ regions accessible to lattice calculations and considerably expanding the region of computability. Revisiting previous lattice results with complete one-loop matching, we obtain the expected partonic threshold behavior---GPDs continuous at $x=\pm \xi$ but with discontinuous derivatives---which has not previously been observed on the lattice. We thus obtain, for the first time, important prediction for GPDs in the distribution-amplitude-like region, which smoothly connects the quark and antiquark PDF-like behaviors.

Comments: 6 pages, 3 figures