Long range rapidity correlations in A+A collisions are sensitive to strong
color field dynamics at early times after the collision. These can be computed
in a factorization formalism \cite{GelisLV5} which expresses the n-gluon
inclusive spectrum at arbitrary rapidity separations in terms of the
multi-parton correlations in the nuclear wavefunctions. This formalism includes
all radiative and rescattering contributions, to leading accuracy in
αsΔY, where ΔY is the rapidity separation between either
one of the measured gluons and a projectile, or between the measured gluons
themselves. In this paper, we use a mean field approximation for the evolution
of the nuclear wavefunctions to obtain a compact result for inclusive two gluon
correlations in terms of the unintegrated gluon distributions in the nuclear
projectiles. The unintegrated gluon distributions satisfy the
Balitsky-Kovchegov equation, which we solve with running coupling and with
initial conditions constrained by existing data on electron-nucleus collisions.
Our results are valid for arbitrary rapidity separations between measured
gluons having transverse momenta p_\perp,q_\perp\gtrsim \qs, where \qs is
the saturation scale in the nuclear wavefunctions. We compare our results to
data on long range rapidity correlations observed in the near-side ridge at
RHIC and make predictions for similar long range rapidity correlations at the
LHC.Comment: 26 pages, 9 figure