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Using the framework that interpolates between the leading power limit of theColor Glass Condensate and the High Energy (or $k_{T}$) factorization wecalculate the direct component of the forward dijet production inultra-peripheral $\mathrm{Pb}$-$\mathrm{Pb}$ collisions at CM energy$5.1\,\mathrm{TeV}$ per nucleon pair. The formalism is applicable when theaverage transverse momentum of the dijet system $P_{T}$ is much bigger than thesaturation scale $Q_{s}$, $P_{T}\gg Q_{s}$, while the imbalance of the dijetsystem can be arbitrary. The cross section is uniquely sensitive to theWeizs\"acker-Williams (WW) unintegrated gluon distribution, which is far lessknown from experimental data than the most common dipole gluon distributionappearing in inclusive small-$x$ processes. We have calculated cross sectionsand nuclear modification ratios using WW gluon distribution obtained from thedipole gluon density through the Gaussian approximation. The dipole gluondistribution used to get WW was fitted to the inclusive HERA data with thenonlinear extension of unified BFKL+DGLAP evolution equation. The saturationeffects are visible but rather weak for realistic $p_{T}$ cut on the dijetsystem, reaching about $20\%$ with the cut as low as $6\,\mathrm{GeV}$. We findthat the LO collinear factorization with nuclear leading twist shadowingpredicts quite similar effects.

Estimating nonlinear effects in forward dijet production in ultra-peripheral heavy ion collisions at the LHC