Gluon quasidistribution function at one loop

Abstract

We study the unpolarized gluon quasidistribution function in the nucleon at one loop level in the large momentum effective theory. For the quark quasidistribution, power law ultraviolet divergences arise in the cut-off scheme and an important observation is that they all are subjected to Wilson lines. However for the gluon quasidistribution function, we first point out that the linear ultraviolet divergences also exist in the real diagram which is not connected to any Wilson line. We then study the one loop corrections to parton distribution functions in both cut-off scheme and dimensional regularization to deal with the ultraviolet divergences. In addition to the ordinary quark and gluon distributions, we also include the quark to gluon and gluon to quark splitting diagrams. The complete one-loop matching factors between the quasi and light cone parton distribution functions are presented in the cut-off scheme. We derive the $P^z$ evolution equation for quasi parton distribution functions, and find that the $P^z$ evolution kernels are identical to the DGLAP evolution kernels.

Figures (8)

• Figure 1: Feynman rules for quasi gluon distribution.
• Figure 2: One-loop real corrections to quasi (light-cone) gluon distribution in Feynman gauge. The double line includes both the gauge link and non-abelian contributions.
• Figure 3: One-loop virtual corrections to quasi (light-cone) gluon distribution in Feynman gauge, the conjugate diagrams are not shown. The double line includes both the gauge link and non-abelian contributions.
• Figure 4: One-loop real corrections to quark quasi (light-cone) distributions in Feynman gauge.
• Figure 5: One-loop virtual corrections to quark quasi (light-cone) distributions in Feynman gauge, where the conjugate diagrams are not shown.