  A clear understanding of nuclear parton distribution functions (nPDFs) plays
a crucial role in the interpretation of collider data taken at the Relativistic
Heavy Ion Collider (RHIC), the Large Hadron Collider (LHC) and in the near
future at the Electron-Ion Collider (EIC). Even with the recent inclusions of
vector boson and light meson production data, the uncertainty of the gluon PDF
remains substantial and limits the interpretation of heavy ion collision data.
To obtain new constraints on the nuclear gluon PDF, we extend our recent
nCTEQ15WZ+SIH analysis to inclusive quarkonium and open heavy-flavor meson
production data from the LHC. This vast new data set covers a wide kinematic
range and puts strong constraints on the nuclear gluon PDF down to $x\lesssim
10^{-5}$. The theoretical predictions for these data sets are obtained from a
data-driven approach, where proton-proton data are used to determine effective
scattering matrix elements. This approach is validated with detailed
comparisons to existing next-to-leading order (NLO) calculations in
non-relativistic QCD (NRQCD) for quarkonia and in the general-mass
variable-flavor-number scheme (GMVFNS) for the open heavy-flavored mesons. In
addition, the uncertainties from the data-driven approach are determined using
the Hessian method and accounted for in the PDF fits. This extension of our
previous analyses represents an important step toward the next generation of
PDFs not only by including new data sets, but also by exploring new methods for
future analyses.
