  Correlations between the momenta of the final state hadrons measured in
proton or nucleus collisions contain information that sheds light on the
initial conditions and evolutionary dynamics of the collision system. These
correlation measurements have revealed the long-range rapidity correlations in
p-p and p-Pb systems, and they have also made it possible to extract the
elliptic flow coefficient from hadron correlation measurements. In this work,
we calculate five- and six-gluon correlation functions in the framework of
saturation physics by using superdiagrams. We also derive the cumulant
expansion of the gluon correlators that is valid in the gluon saturation limit.
We show that the cumulant expansion of the gluon correlators that is used for
counting the number of diagrams to be calculated does not follow the standard
cumulant expansion. We also explain how these findings can be used in obtaining
experimentally relevant observables such as flow coefficients calculated from
correlations as well as ratios of the correlation functions of different
orders.
