  The study of a quasi back-to-back isolated pair made of a heavy quarkonium,
such as a J/psi or a Upsilon, and a photon produced in proton-proton collisions
at the LHC, is probably the optimal way to get right away a first experimental
determination of two gluon transverse-momentum-dependent distributions (TMDs)
in an unpolarized proton, f1^g and h1^perp,g the latter giving the distribution
of linearly polarized gluons. To substantiate this, we calculate the
transverse-momentum-dependent effects that arise in the process under study and
discuss the feasibility of their measurements.
