  A quantitative estimate is presented for the double transverse spin
asymmetries at measured q_T in both the Drell-Yan process and W-boson
production due to Transverse Momentum Dependent (TMD) effects. These spin
asymmetries are calculated as a function of the lepton azimuthal angle as
measured in the laboratory frame. In this frame, in contrast to the
Collins-Soper frame, the TMD effects contribute to the spin asymmetry
A_{TT}(q_T) in the same way as transversity does, which makes them a background
for transversity measurements in the Drell-Yan process and new physics studies
in W-boson production. Using the current knowledge of the relevant TMDs we
conclude that this background is negligible and, therefore, will not hamper
transversity measurements nor new physics studies when performed in the
laboratory frame. We also point out a cross-check asymmetry measurement to
bound the TMD contributions, which is independent of assumptions on the sizes
of the relevant TMDs.

High Energy Physics - Phenomenology