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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. 

