One-loop matching for generalized parton distributions

We present the one-loop matching condition for the unpolarized and polarized generalized quark distributions in the nonsinglet case. The matching condition links the quasi distributions defined in terms of spacelike correlators at finite nucleon momentum to the light-cone distributions, and it is useful for extracting the latter from the former in a lattice QCD calculation. Our results show that at one-loop and leading power accuracy the matching for the light-cone generalized quark distribution $H$ ($\tilde{H}$) is nontrivial, whereas no matching is required for $E$ ($\tilde{E}$). Therefore, $E$ ($\tilde{E}$) can be smoothly approached by its quasi counterpart in the large momentum limit. We also present the matching for the distribution amplitude of the pion.

Figure 1

One-loop diagrams for GPDs in the axial gauge.