GTMDs and the factorization of exclusive double Drell-Yan

Abstract

Different exclusive processes have been proposed to access the generalized transverse momentum dependent distributions (GTMDs) with no proof of factorization, which allows to rigorously define the GTMDs. Using Soft Collinear Effective Theory we derive for the first time the factorization of the differential cross section for the exclusive double Drell-Yan process π N → N′γ ∗γ ∗ → N′( + −)( + −), for small transverse momenta of the photons in terms of a perturbatively calculable hard factor, GTMDs and light-cone wave functions (LCWFs). We find that the hard factor of the process can be obtained from single inclusive Drell-Yan production so that one can resum logarithms at high orders in QCD. We also discuss the evolution of the GTMDs and the LCWFs.