Charged 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 systematic uncertainties of the Higgs boson cross section predictions by 50% over a broad range of Higgs boson rapidities.
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