  Lepton pairs are produced copiously in high-energy hadron collisions via
electroweak gauge boson exchange, and are one of the most precisely measured
final states in proton-proton collisions at the Large Hadron Collider (LHC). We
propose that measurements of lepton angular distributions can be used to
improve the accuracy of theoretical predictions for Higgs boson production
cross sections at the LHC. To this end, we exploit the sensitivity of the
lepton angular coefficient associated with the longitudinal Z-boson
polarization to the parton density function (PDF) for gluons resolved from the
incoming protons, in order to constrain the Higgs boson cross section from
gluon fusion processes. By a detailed numerical analysis using the open-source
platform xFitter, we find that high-statistics determinations of the
longitudinally polarized angular coefficient at the LHC Run III and
high-luminosity HL-LHC improve the PDF systematics of the Higgs boson cross
section predictions by 50 % over a broad range of Higgs boson rapidities.
