QCD transverse-momentum resummation in gluon fusion processes

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_T) distribution of the system in the small-q_T region (q_T << M), and we present a study of the perturbative QCD contributions that are enhanced by powers of large logarithmic terms of the type ln (M^2/q_T^2). 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 (qqbar) annihilation and/or by gluon fusion. The resummation formalism for the qqbar annihilation subprocess is well established, and it is usually extrapolated to the gluon fusion subprocess. We point out that this naive extrapolation is not correct, and we present the all-order resummation formula for the q_T distribution in gluon fusion processes. The gluon fusion resummation formula has a richer structure than the resummation formula in qqbar 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_T cross section at small values of q_T, 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.