  The interplay between the small x limit of QCD amplitudes and QCD
factorization at moderate x has been studied extensively in recent years. It
was finally shown that semiclassical formulations of small x physics can have
the form of an infinite twist framework involving Transverse Momentum Dependent
(TMD) distributions in the eikonal limit. In this work, we demonstrate that
small x distributions can be formulated in terms of transverse gauge links.
This allows in particular for direct and efficient decompositions of
observables into subamplitudes involving gauge invariant sub-operators which
span parton distributions.
