  We investigate possible signatures of gluon saturation using forward $p+A \to
j+j+X$ di-jet production processes at the Large Hadron Collider. In the forward
rapidity region, this is a highly asymmetric process where partons with large
longitudinal momentum fraction \(x\) in the dilute projectile are used as a
probe to resolve the small \(x\) partonic content of the dense target. Such
dilute-dense processes can be described in the factorization framework of
Improved Transverse Momentum Distributions (ITMDs). We present a new model for
ITMDs where we explicitly introduce the impact parameter (\(b\)) dependence in
the ITMDs, to properly account for the nuclear enhancement of gluon saturation
effects, and discuss the phenomenological consequences for $p-Pb$, $p-Xe$ and
$p-O$ collisions at the LHC. While the case of $p-p$ and $e-p$ collisions is
used to fix the model parameters, we find that, on average, the nuclear
enhancement of the saturation scale is noticeably weaker than expected from
naive scaling with a simple dependence on the atomic number. Since our model
explicitly accounts for event-by-event fluctuations of the nuclear geometry, it
can also be applied to study forward central correlations in $p-A$ collisions.
