We derive a factorization theorem for Drell-Yan process at low q T 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 α s 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 α s . The factorization theorem is validated to first order in α s and also the gauge invariance between Feynman and light-cone gauges.

We study the QCD evolution of the Sivers effect in both semi-inclusive deep inelastic scattering (SIDIS) and Drell-Yan production (DY). We pay close attention to the non-perturbative spinindependent Sudakov factor in the evolution formalism and find a universal form which can describe reasonably well the experimental data on the transverse momentum distributions in SIDIS, DY lepton pair and W/Z production. With this Sudakov factor at hand, we perform a global fitting of all the experimental data on the Sivers asymmetry in SIDIS from HERMES, COMPASS and Jefferson Lab. We then make predictions for the Sivers asymmetry in DY lepton pair and W production that can be compared to the future experimental measurements to test the sign change of the Sivers functions between SIDIS and DY processes and constrain the sea quark Sivers functions.

We discuss the evolution of the eight leading twist transverse momentum dependent parton distribution functions, which turns out to be universal and spin independent. By using the highest order perturbatively calculable ingredients at our disposal, we perform the resummation of the large logarithms that appear in the evolution kernel of transverse momentum distributions up to next-to-next-to-leading logarithms (NNLL), thus obtaining an expression for the kernel with highly reduced model dependence. Our results can also be obtained using the standard CSS approach when a particular choice of the b * prescription is used. In this sense, and while restricted to the perturbative domain of applicability, we consider our results as a "prediction" of the correct value of bmax which is very close to 1.5 GeV −1 . We explore under which kinematical conditions the effects of the non-perturbative region are negligible, and hence the evolution of transverse momentum distributions can be applied in a model independent way. The application of the kernel is illustrated by considering the unpolarized transverse momentum dependent parton distribution function and the Sivers function.

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.

We present an effective field theory approach to resum the large double logarithms originated from soft-gluon radiations at small final-state hadron invariant masses in Higgs and vector boson (γ * , W, Z) production at hadron colliders. The approach is conceptually simple, independent of details of an effective field theory formulation, and valid to all orders in sub-leading logarithms.As an example, we show the result of summing the next-to-next-to-next-to leading logarithms is identical to that of the standard pQCD factorization method.