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.
Highlights
Hadron structures are determined by strong interactions among quarks and gluons
Are the same in Eqs. (15) and (16). It indicates that the quasi and light-cone distributions have the same infrared structure, and the large momentum effective theory (LaMET) factorization holds for the gluon case at one-loop level
We have investigated the unpolarized gluon quasidistribution function in the nucleon at one loop level in the large momentum effective theory
Summary
Hadron structures are determined by strong interactions among quarks and gluons. In order to make predictions for high energy process involving hadrons, one must rely the factorization approach. One may appeal to some theoretical parametrization of PDFs and fit the free parameters in the parametrization using the experiment data such as DIS and pp collisions data [1,2,3] Such an approach has reached very high accuracy, for instance one has taken into account the next-to-next-to-leading order in αs for the calculation of partonic cross section. In 2013, a new approach named as the large momentum effective theory (LaMET) was proposed [4,5] to determine parton distribution functions on the lattice In this approach, instead of using the correlations of quarks and gluons on the light cone, one makes use of the matrix elements of frame-dependent equal-time correlators in the large momentum limit. 3, we give the one loop matching results for parton quasidistributions and light cone distributions at the dimensional regularization scheme (DR). We have used the finite gluon mass to regulate the infrared divergences, while in the Appendix C, we present the results with the offshellness as an infrared regulator
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