Soft and Collinear Factorization and Transverse Momentum Dependent Parton Distribution Functions

Abstract

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.

Comments: 9 pages, 3 figures. We modified the discussion about the equivalence between Collins (JCC) and Echevarria-Idilbi-Scimemi (EIS) definitions of TMDPDF. The results remain intact. Version to appear in Phys. Lett. B