  We consider photon pair production in hadronic collisions at large mass and
small transverse momentum of the pair, assuming that factorization in terms of
transverse momentum dependent parton distributions applies. The unpolarized
cross section is found to have azimuthal angular dependencies that are
generated by a gluonic version of the Boer-Mulders function. In addition, the
single-transversely polarized cross section is sensitive to the gluon Sivers
function. We present simple numerical estimates for the Boer-Mulders and Sivers
effects in diphoton production at RHIC and find that the process would offer
unique opportunities for exploring transverse momentum dependent gluon
distributions.
