  We study two-particle long-range rapidity correlations arising in the early
stages of heavy ion collisions in the saturation/Color Glass Condensate
framework, assuming for simplicity that one colliding nucleus is much larger
than the other. We calculate the two-gluon production cross section while
including all-order saturation effects in the heavy nucleus with the
lowest-order rescattering in the lighter nucleus. We find four types of
correlations in the two-gluon production cross section: (i) geometric
correlations, (ii) HBT correlations accompanied by a back-to-back maximum,
(iii) away-side correlations, and (iv) near-side azimuthal correlations which
are long-range in rapidity. The geometric correlations (i) are due to the fact
that nucleons are correlated by simply being confined within the same nucleus
and may lead to long-range rapidity correlations for the produced particles
without strong azimuthal angle dependence. Somewhat surprisingly, long-range
rapidity correlations (iii) and (iv) have exactly the same amplitudes along
with azimuthal and rapidity shapes: one centered around \Delta \phi =\pi\ with
the other one centered around \Delta \phi =0 (here \Delta \phi\ is the
azimuthal angle between the two produced gluons). We thus observe that the
early-time CGC dynamics in nucleus-nucleus collisions generates azimuthal
non-flow correlations which are qualitatively different from jet correlations
by being long-range in rapidity. If strong enough, they have the potential of
mimicking the elliptic (and higher-order even-harmonic) flow in the di-hadron
correlators: one may need to take them into account in the experimental
determination of the flow observables.
