  Since its start of data taking, the LHC has provided an impressive wealth of
information on the quark and gluon structure of the proton. Indeed, modern
global analyses of parton distribution functions (PDFs) include a wide range of
LHC measurements of processes such as the production of jets, electroweak gauge
bosons, and top quark pairs. In this work, we assess the ultimate constraining
power of LHC data on the PDFs that can be expected from the complete dataset,
in particular after the High-Luminosity (HL) phase, starting in around 2025.
The huge statistics of the HL-LHC, delivering $\mathcal{L}=3$ ab$^{-1}$ to
ATLAS and CMS and $\mathcal{L}=0.3$ ab$^{-1}$ to LHCb, will lead to an
extension of the kinematic coverage of PDF-sensitive measurements as well as to
an improvement in their statistical and systematic uncertainties. Here we
generate HL-LHC pseudo-data for different projections of the experimental
uncertainties, and then quantify the resulting constraints on the PDF4LHC15 set
by means of the Hessian profiling method. We find that HL-LHC measurements can
reduce PDF uncertainties by up to a factor of 2 to 4 in comparison to
state-of-the-art fits, leading to few-percent uncertainties for important
observables such as the Higgs boson transverse momentum distribution via
gluon-fusion. Our results illustrate the significant improvement in the
precision of PDF fits achievable from hadron collider data alone, and motivate
the continuation of the ongoing successful program of PDF-sensitive
measurements by the LHC collaborations.
