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Using the small-$x$ Improved Transverse Momentum Dependent factorization(ITMD), which, for a general two-to-two massless scattering can be provedwithin the Color Glass Condensate (CGC) theory for transverse momenta ofparticles greater than the saturation scale, we provide predictions forisolated forward photon and jet production in proton-proton and proton-nucleuscollisions within the planned ALICE FoCal detector acceptance. We studyazimuthal correlations, $p_T$ spectra, as well as normalized ratios ofproton-proton cross sections for different energies. The only TMD distributionneeded for that process is the "dipole" TMD gluon distribution, which in ourcomputations is based on HERA data and undergoes momentum space BK evolutionequation with DGLAP corrections and Sudakov resummation. We conclude, that theprocess provides an excellent probe of the dipole TMD gluon distribution insaturation regime.

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