  We obtain prompt di-photon cross-section in proton-nucleus collisions in
Hamiltonian light-cone approach within a hybrid approximation, treating the
projectile proton in the parton model and the target nucleus in the
Color-Glass-Condensate approach. We study in details the di-photon correlations
in quark-nucleus and proton-nucleus collisions at RHIC and the LHC. We show
that the single fragmentation di-photon produces the away side correlations
peak, and the double fragmentation component of prompt di-photon is responsible
for the near-side peak, and the long-range in rapidity near-side azimuthal
collimation, the so-called "ridge" structure. We study the transverse momentum,
density and energy dependence of the di-photon ridge and show that it strongly
depends on the kinematics and saturation dynamics. We show that while di-photon
ridge exists at the LHC in quark-nucleus collisions, the effect disappears in
proton-nucleus collisions at the LHC. At RHIC the ridge-type structure persists
at low transverse momenta of di-photon even in proton-nucleus collisions. We
argue that di-photon correlation measurments in p+A collisions can help to
discriminate among models and understand the true origin of the observed
di-hadron ridge in p+A collisions. We also show that in addition to the ridge
structure, prompt di-photon correlation also exhibits some distinct novel
features, including the emergence of away side double-peak structure at
intermediate transverse momenta.
