Nuclear PDF constraints from p+Pb collisions at the LHC

As the current nuclear PDF analyses are mainly constrained by fixed-target Drell-Yan and deeply inelastic scattering data only the quark nuclear modifications at fairly large $x$ values are in a good control. Inclusive pion production in d+Au collisions at RHIC provides some constraints for gluons but due to the limited kinematic reach of the data the gluon modifications remain uncertain especially at small values of $x$. In this talk, we discuss how the existing data from p+Pb collisions at the LHC can improve the nuclear PDF fits and which measurements would be sensitive to the small-$x$ gluons. In particular, we consider inclusive hadron production, compare this to direct photons, and show estimates of the effect of CMS dijet measurements to the uncertainty of nuclear gluon distributions.