  We construct a quark target model (QTM) to incorporate intrinsic glue into
effective low-energy models of QCD, which often contain only quark degrees of
freedom. This method guarantees the gauge invariance of observables
order-by-order in the strong coupling. The quark and gluon PDFs for the dressed
quarks are obtained in the QTM at leading order. We demonstrate gauge
invariance of the results by comparing both covariant and light cone gauges,
with the former including an explicit Wilson line contribution. A key finding
is that in covariant gauges the Wilson line can carry a significant amount of
the light cone momentum. With coupling strength $\alpha_s = 0.5$ and dressed
quark mass $M_q = 0.4\,$GeV, we find quark and gluon momentum fractions of
$\left<x\right>_q = 0.81$ and $\left<x\right>_g = 0.19$, where the Wilson line
contribution to the quark momentum fraction is $-0.18$. We use the on-shell
renormalization scheme and find that at one-loop this Wilson line contribution
does not depend on the covariant gauge but does vanish in light cone gauge as
expected. This result demonstrates that it is crucial to account for Wilson
line contributions when calculating quantum correlation functions in covariant
gauges. We also consider the impact of a gluon mass using the gauge invariant
formalism proposed by Cornwall, and combine these QTM results with two
quark-level models to obtain quark and gluon PDFs for the pion.
