We consider the production of a generic system of non-strongly interacting particles with a high total invariant mass M in hadron collisions. We examine the transverse-momentum (q) distribution of the system in the small-q region (q≪M), and we present a study of the perturbative QCD contributions that are enhanced by powers of large logarithmic terms of the type ln(M2/qT2). These terms can be resummed to all orders in QCD perturbation theory. The partonic production mechanism of the final-state system can be controlled by quark-antiquark (qq¯) annihilation and/or by gluon fusion. The resummation formalism for the qq¯ annihilation subprocess is well established, and it is usually extrapolated to the gluon fusion subprocess. We point out that this naïve extrapolation is not correct, and we present the all-order resummation formula for the q distribution in gluon fusion processes. The gluon fusion resummation formula has a richer structure than the resummation formula in qq¯ annihilation. The additional structure originates from collinear correlations that are a specific feature of the evolution of the colliding hadrons into gluon partonic states. In the q cross section at small values of q, these gluon collinear correlations produce coherent spin correlations between the helicity states of the initial-state gluons and definite azimuthal-angle correlations between the final-state particles of the observed high-mass system.