Factorization theorem for Drell-Yan at low qT and transverse-momentum distributions on-the-light-cone

We derive a factorization theorem for Drell-Yan process at low qT using effective field theory methods. In this theorem all the obtained quantities are gauge invariant and the special role of the soft function — and its subtraction thereof — is emphasized. We define transverse-momentum dependent parton distribution functions (TMDPDFs) which are free from light-cone singularities while all the Wilson lines are defined on-the-light-cone. We show explicitly to first order in αs that the partonic Feynman PDF can be obtained from the newly defined partonic TMDPDF by integrating over the transverse momentum of the parton inside the hadron. We obtain a resummed expression for the TMDPDF, and hence for the cross section, in impact parameter space. The universality of the newly defined matrix elements is established perturbatively to first order in αs. The factorization theorem is validated to first order in αs and also the gauge invariance between Feynman and light-cone gauges.