Production of electroweak gauge bosons at forward rapidities in the color - dipole $S$ - matrix framework

The cross-section for the production of an electroweak gauge boson ($G = W^{\pm}, Z^0, \gamma$) at forward rapidities in $pp$ collisions is derived within the color - dipole $S$ - matrix framework. We present the full expressions for the differential cross-section of the $q p \rightarrow G X$ process in the impact parameter and transverse momentum spaces, considering the longitudinal and transverse polarizations of the gauge boson. The particular cases associated with the Drell - Yan process and real photon production are discussed. We demonstrate that the final formulae are expressed in terms of the dipole - proton cross-section or the unintegrated gluon distribution, and can be used to estimate the impact of the saturation effects in the gauge boson production at the LHC and future colliders.