  The azimuthal asymmetry of heavy quarks production on double polarized
proton-proton and proton-antiproton colliders are studied in this work at
next-to-leading order in $\alpha_s$, with some details included. The purpose is
to see whether the effect of extracted transversity distribution functions can
be seen on present and near future colliders. All analytic one-loop hard
coefficients are given. Numerical results for the asymmetry on
proton-(anti)proton colliders are presented.
