  The dependence of the top-quark mass measurement in top-quark production on
the parton distribution functions is explored through the differential
distribution of the invariant mass of the top-antitop system in top-quark pair
production at hadron colliders. Several different proton-proton collider
options are considered: 8 TeV, 13 TeV, 13.6 TeV, 14 TeV, and 100 TeV. The
top-quark mass is obtained from a chi-squared fit to the invariant mass of the
top-antitop-quark pair. The parton distribution function uncertainties are used
in the chi-square evaluation. The uncertainties are reduced through a fit to
the longitudinal momentum of the top-antitop system. The top-quark mass
uncertainty due to parton distribution functions is found to be reduced by 20%.
