Abstract
Recent perturbative calculation of quasi gluon distribution function at one-loop level shows the existence of extra linear ultraviolet divergences in the cut-off scheme. We employ the auxiliary field approach, and study the renormalization of gluon operators. The non-local gluon operator can mix with new operators under renormalization, and the linear divergences in quasi distribution function can be into the newly introduced operators. After including the mixing, we find the improved quasi gluon distribution functions contain only logarithmic divergences, and thus can be used to extract the gluon distribution in large momentum effective theory.
Highlights
It is shown that linear divergences exist even in the diagrams without any Wilson line, and these linear divergences can not be absorbed into the renormalization of Wilson line
The power divergence in this diagram can be viewed as the product of two linear divergences, which are from the one-loop corrections of the gluon-Wilson line vertices
Eq (4.25) indicates that, if one defines quasi gluon distribution by specifying μ and ν components of gluonium operator, the renormalization of logarithm divergence will be greatly simplified when the tangents of the contour are collinear to the projection vector corresponding to these components; on the other hand, if one modifies the contour of the Wilson line, it is more convenient to modify the components of gluon strength tensor correspondingly
Summary
We adopt a modified definition, where the Lorentz index of gluon field strength tensor is summed over all the directions except “3”, i.e., fg/H (x, μ) =. Under the P z → ∞ limit, one can obtain dx xfg/H (x, μ) = dx xfg/H (x, P z, μ) This relation can be generalized to high order moments, and to the distribution functions f and fthemselves. It indicates that eq (2.4) is a reasonable definition of quasi gluon distribution. In the large P z limit, the − component is suppressed and the operator for quasi-PDF recovers the same Lorentz structure with the light-cone PDF. The factor 1/2 arises from the conversion of Euclidean and light-cone coordinates
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
