Relating Transverse Momentum Dependent and Collinear Factorization   Theorems in a Generalized Formalism
  We construct an improved implementation for combining transverse-momentum-dependent (TMD) factorization and collinear factorization. TMD factorization is suitable for low transverse momentum physics, while collinear factorization is suitable for high transverse momenta and for a cross section integrated over transverse momentum. The result is a modified version of the standard $W+Y$ prescription traditionally used in the Collins-Soper-Sterman (CSS) formalism and related approaches. We further argue that questions regarding the shape and $Q$-dependence of the cross sections at lower $Q$ are largely governed by the matching to the $Y$-term. 
J. Collins, L. Gamberg, A. Prokudin, T. C. Rogers, N. Sato, and B.   Wang
hep-ph