  Theoretically there are two approaches to predict single spin azimuthal
asymmetries. One is to take transverse momenta of partons into account by using
transverse momentum dependent parton distributions, while another is to take
asymmetries as a twist-3 effect. The nonperturbative effects in these
approaches are parameterized with different matrix elements and predictions can
be different. Recently, gauge invariant definitions of transverse momentum
dependent parton distributions were derived. With these definitions it can be
shown that there are relations between nonperturbative matrix elements in two
approaches. These relations may enable us to unify two approaches and to have
unique predictions for single spin azimuthal asymmetries.In this letter we
derive these relations by using time-reversal symmetry and show that even with
these relations the single spin azimuthal asymmetry in Drell-Yan process is
predicted differently in different approaches.
