  We consider two different spin asymmetries in Drell-Yan processes generated
by the collisions of an unpolarized proton beam on transversely polarized
protons: the muon helicity asymmetry and the left-right asymmetry. We calculate
the asymmetries in the framework of the QCD improved parton model, taking into
account the parton transverse momentum and considering the first order QCD
corrections. The muon helicity asymmetry is sensitive to the quark transversity
distribution and is nonvanishing even at zero order. On the contrary the
left-right asymmetry vanishes at zero order but not at first order in the QCD
coupling constant, as a result of gluon contribution.
