TMD-Factorization in Hadron-Hadron Collision

Proof of transverse-momentum-dependent(TMD) factorization for hadron-hadron collision is given in this paper. We focus on processes without detected soft final hadrons or detected final hadrons that are collinear to initial hadrons. This contradicts the widely accepted viewpoint that TMD- factorization does not hold in such processes even in the generalized sense. The key point is that singular points of the type l+ = 0 can be absorbed into Wilson lines of soft gluons, where l is collinear to the plus direction. Thus one should subtract such singular points from the collinear region of l. After such subtraction, one can make use of Ward identity to absorb effects of scalar-polarized collinear gluons into Wilson lines.