  Transverse momentum broadening of a parton propagating through a large
nucleus is evaluated in the color dipole approach using different models for
the dipole cross section or unintegrated gluon distribution, which lead to
different values of the coefficient $C_{\mathcal{F}}(0,s)$. Numerical
calculations are compared to data extracted from LHCb and ALICE experiments for
nuclear broadening of $J/\psi$. We find that different models which describe
the small-$x$ data predict values of $\Delta p_T^2$ that agree reasonably well
with experiment, specially for forward rapidity. The centrality dependence was
also analysed and the models are consistent with the ALICE measurements.
