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[31] Because in Eq. (4) there is an integration over all k 1 T , one generally must be careful in treating the region where the t goes to zero in the hard part. For this paper, we are specifically interested in the collinear region where k 1 T is small, so we will assume that any contribution from t close to zero is removed by a cutoff on large k 1 T . 

[32] In a general proof of factorization, one may need to worry about cancellations in the “supersoft” region, k 1 T << Λ QCD , since we are now using a massless theory, in con- trast to Ref. [17]. In this paper, we are concerned mainly with gluons with k 1 T ∼ Λ QCD so these issues do not affect our argument. 

[33] In earlier sections we neglected gluon exchanges between active quarks because they do not lead to spin depen- dence. In the unpolarized cross section, the complete re- sult is obtained only after including interactions between active quarks. In the collinear regions they result in the same set of eikonal factors as in Eqs. (25, 26) and anal- ogous Wilson line contributions. The key point is that the usual steps that normally would lead to a cancella- tion of the factorization anomaly between different cuts of the same graph in collinear factorization, fails in the 

