  We consider the associated production of a vector or Higgs boson with a jet
in hadronic collisions. When the transverse momentum $q_T$ of the boson-jet
system is much smaller than its invariant mass $Q$, the QCD perturbative
expansion is affected by large logarithmic terms that must be resummed to all
orders. We discuss the all-order resummation structure of the logarithmically
enhanced contributions up to next-to-leading logarithmic accuracy. Resummation
is performed at the differential level with respect to the kinematical
variables of the boson-jet system. Soft-parton radiation produces azimuthal
correlations that are fully accounted for in our framework. We present explicit
analytical results for the resummation coefficients up to next-to-leading order
and next-to-leading logarithmic accuracy, that include the exact dependence on
the jet radius.
