Double Spin Asymmetries in P-wave Charmonium Hadroproduction

We discuss the double spin asymmetries in P-wave charmonium hadroproduction with non-zero transverse momenta at fixed target energies, $\sqrt{s}\simeq40$ GeV, within the framework of the NRQCD factorization approach. The size of the asymmetries and the projected statistical errors in a future option of HERA with longitudinally polarized protons scattering off a polarized target (HERA-$\vec N$) are calculated. Measurements of the $\chi_{c1}$ and $\chi_{c2}$ decays into dilepton plus photon should allow to distinguish between different parametrizations for the polarized gluon distribution in the proton. At higher energies ($\sqrt{s}=200$ GeV) the situation appears less favourable with the presently envisaged integrated luminosities of the polarized RHIC collider.