10 FIG. 5: A gluon three-point interaction that contributes to the single gluon Wilson line attachment. FIG. 6: Graphs that contribute to the standard Wilson lines at the level of two extra gluons. The Hermitian conjugate graphs should also be included, as well as graphs with both gluons collinear to p 2 . terms constrains the possible generalizations of TMD- factorization, as we will discuss more in Sect. V. The simple color structure of the hard process strongly limits the number of non-vanishing graphs. All graphs in which the second gluon is internal to the hadron sub- graph (e.g. Fig. 5) only give further contributions to a single gluon contribution in the standard Wilson lines in Eq. (24). The only non-vanishing graphs that give order g 2 contributions to a Wilson line operator are of the type shown in Figs. 6, 7, 8. All other graphs vanish because they include an overall color factor Tr$_{C}$ [ t $^{a}$] = 0. We will consider each type of graph in turn in the next few subsections. We will first identify the graphs that are consistent with the standard TMD-factorization formula Eq. (24). Next we will consider the graphs that contribute to a violation of standard TMD-factorization that were already discussed in Refs. [18]. The remaining graphs in Fig. 8 are ultimately responsible for breaking generalized factorization, so we will put off any further discussion of them until Sect. VI. k 2 p 2 p 1 k 3 k 4 l k 1 − l p 2 p 1 k 3 k 4 l 1 l 2 k 2 − l 2 k 1 − l 1 p 2 p 1 k 3 k 4 l 1 l 2 k 2 − l 2 k 1 − l 1 (a) (b) k 2 p 2 p 1 k 3 k 4 l 2 l 1 k 1 − l 1 − l 2 k 2 p 2 p 1 k 3 k 4 l 1 l 2 k 1 − l 2 k 1 − l 1 (c) (d)