  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.
