  In this talk, we present a way to improve the accuracy of theoretical
predictions for Higgs boson production cross sections at the LHC using the
measurements of lepton angular distributions. In this regards, 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. We find that high-statistics determinations of the
longitudinally polarized angular coefficient at the LHC Run 3 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. This
study has been conducted using the open-source fitting framework xFitter. This
talk refers to the following paper: arXiv:2012.10298[hep-ph]
