Accessing Sivers gluon distribution via transverse single spin asymmetries in p(transv. polarized) p --> D X processes at RHIC

The production of D mesons in the scattering of transversely polarized protons off unpolarized protons at RHIC offers a clear opportunity to gain information on the Sivers gluon distribution function. D production at intermediate rapidity values is dominated by the elementary g g --> c cbar channel; contributions from q qbar --> c cbar s-channel become important only at very large values of x_F. In both processes there is no single spin transfer, so that the final c or cbar quarks are not polarized. Therefore, any transverse single spin asymmetry observed for D's produced in p(transv. polarized) p interactions cannot originate from the Collins fragmentation mechanism, but only from the Sivers effect in the distribution functions. In particular, any sizeable spin asymmetry measured in p(transv. polarized) p --> D X at mid-rapidity values will be a direct indication of a non zero Sivers gluon distribution function. We study the p(transv. polarized) p --> D X process including intrinsic transverse motion in the parton distribution and fragmentation functions and in the elementary dynamics, and show how results from RHIC could allow a measurement of the Sivers gluon distribution function.