We calculate the single transverse-spin asymmetry for open charm production in $pp$ collisions within the QCD collinear factorization approach. We include contributions from both twist-three quark-gluon and tri-gluon correlation functions. We find th
at the quark-gluon correlation functions alone generate only a very small asymmetry for open charm production in the kinematic region of current interest at RHIC, so that the observation of any significant single-spin asymmetry would be a clear indication of the presence of tri-gluon correlations inside a polarized proton. We furthermore demonstrate that the tri-gluon contribution could be very different for the production of $D$ and $bar{D}$ mesons. These features make the single spin asymmetry in open charm production in polarized $pp$ collisions at RHIC an excellent probe of tri-gluon correlation functions.
We study the single-transverse spin asymmetry for open charm production in the semi-inclusive lepton-hadron deep inelastic scattering. We calculate the asymmetry in terms of the QCD collinear factorization approach for $D$ mesons at high enough $P_{h
perp}$, and find that the asymmetry is proportional to the twist-three tri-gluon correlation function in the proton. With a simple model for the tri-gluon correlation function, we estimate the asymmetry for both COMPASS and eRHIC kinematics, and discuss the possibilities of extracting the tri-gluon correlation function in these experiments.
