Glauber Gluons in Soft Collinear Effective Theory and Factorization of Drell-Yan Processes

Glauber gluons in Drell-Yan processes are soft gluons with the transverse momenta much larger than their momentum components along the directions of initial hadrons. Their existence has been a serious challenge in proving the factorization of Drell-Yan processes. The recently proposed soft collinear effect theory of QCD can provide a transparent way to show factorizations for a class of processes, but it does not address the effect of glauber gluons. In this letter we first confirm the existence of glauber gluons through an example. We then add glauber gluons into the effective theory and study their interaction with other particles. In the framework of the effective theory with glauber gluons we are able to show that the effects of glauber gluons in Drell-Yan processes are canceled and the factorization holds in the existence of glauber gluons. Our work completes the proof or argument of factorization of Drell-Yan process in the framework of the soft collinear effective theory.