QCD factorization of quasi generalized gluon distributions

We study the factorization relations between quasi gluon GPDs and twist-2 GPDs. The perturbative coefficient functions are obtained at one-loop level. They are free from any collinear- or I.R. divergences. Unlike the case of the factorization of quasi quark GPDs at one-loop, we have to add ghost contributions for the factorization of quasi gluon GPDs in order to obtain gauge-invariant results. In general, operators will be mixed beyond tree-level. Our work shows that the mixing pattern of the nonlocal operators in quasi gluon GPDs is the same as those of local operators, i.e., the nonlocal operators considered are mixed with gauge-invariant operators, BRST-variation operators and operators involving EOM operator. The factorization relations are obtained for all quasi gluon GPDs. Taking the forward limit, we also obtain the relations between quasi gluon PDFs and twist-2 PDFs.

Automated summary

We studied the factorization relations between quasi gluon GPDs and twist-2 GPDs. Perturbative coefficient functions were obtained at one-loop level, free from any collinear or I.R. divergences. Ghost contributions were added for the factorization of quasi gluon GPDs to obtain gauge-invariant results. Our work showed that the mixing pattern of nonlocal operators in quasi gluon GPDs is the same as that of local operators, involving gauge-invariant operators, BRST-variation operators, and operators with EOM operator. The factorization relations were obtained for all quasi gluon GPDs, and the relations between quasi gluon PDFs and twist-2 PDFs were also derived by taking the forward limit.