Soft and Collinear Factorization and Transverse Momentum Dependent   Parton Distribution Functions
  In this work we consider how a parton distribution function, with an explicit transverse momentum dependence can be properly defined in a regularization-scheme independent manner. We argue that by considering a factorized form of the transverse momentum dependent spectrum for the production of a heavy lepton pair in Drell-Yan reaction, one should first split the relevant soft function into two boost invariant contributions. When those soft contributions are added to the pure collinear contributions, well-defined hadronic matrix elements emerge, i.e., the transverse momentum dependent distributions. We also perform a comparison with Collins' definition. 
Miguel G. Echevarria, Ahmad Idilbi, Ignazio Scimemi
hep-ph