  We discuss possible origins of transverse spin asymmetries in hadron-hadron
collisions and propose an explanation in terms of a chiral-odd T-odd
distribution function with intrinsic transverse momentum dependence, which
would signal a correlation between the transverse spin and the transverse
momentum of quarks inside an unpolarized hadron. We will argue that despite its
conceptual problems, it can account for single spin asymmetries, for example in
p + p(transversely polarized) -> pion + X, and at the same time for the large
cos(2 phi) asymmetry in the unpolarized Drell-Yan cross section, which still
lacks understanding. We use the latter asymmetry to arrive at a crude model for
this function and show explicitly how it relates unpolarized and polarized
observables in the Drell-Yan process, as could be measured with the
proton-proton collisions at RHIC. Moreover, it would provide an alternative
method of accessing the transversity distribution function h_1. For future
reference we also list the complete set of azimuthal asymmetries in the
unpolarized and polarized Drell-Yan process at leading order involving T-odd
distribution functions with intrinsic transverse momentum dependence.
