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.

On the power divergence in quasi gluon distribution function

“…A first calculation of perturbative coefficient for quasi gluon distribution is presented in ref. [56], in which the results are presented in both the cutoff and dimensional regularization (DR) schemes. It is shown that linear divergences exist even in the diagrams without any Wilson line, and thus these linear divergences can not be absorbed into the renormalization of Wilson line.…”

“…According to refs. [6,48,56], i sums over the transverse directions. In this paper, we adopt a modified definition, where the Lorentz index of gluon field strength tensor is summed over all the directions except "3", i.e.,…”

“…JHEP05 (2018)142 [56], the non-Abelian term is combined with the Wilson line. In the present work, the contributions from these two parts are separated.…”

“…At last we note that there are also contributions from crossed diagrams, which have been discussed in ref. [56]. These contributions can be easily derived by using the propertỹ f (−x) = −f (x).…”

“…In ref. [56], we have calculated the matching coefficient in the dimensional regularization scheme. It is interesting to notice that the differences between the cut-off and DR schemes only reside in the linearly divergent terms, while the finite terms are the same.…”