Forward $\gamma$+jet production in proton-proton and proton-lead collisions at LHC within the FoCal calorimeter acceptance

Using the small-$x$ Improved Transverse Momentum Dependent factorization, which can be proved within the Color Glass Condensate theory for transverse momenta of particles greater than the saturation scale, we provide predictions for isolated forward photon and jet production in proton-proton and proton-nucleus collisions within the planned ALICE FoCal detector acceptance. We study azimuthal correlations, $p_T$ spectra, as well as normalized ratios of proton-proton cross sections for different energies. We conclude, that the process provides an excellent probe of the dipole transverse momentum dependent gluon distribution in saturation regime.