An exploratory study of the impact of CMS double-differential top distributions on the gluon parton distribution function

LHC $t\overline{t}$ data have the potential to provide constraints on the gluon distribution, especially at high x, with both ATLAS and CMS performing differential measurements. Recently, CMS has measured double-differential $t\overline{t}$ distributions at 8 TeV. In this paper we examine the impact of this data set on the gluon distribution. To that end we develop novel, double-differential NNLO predictions for that data. No significant impact is found when the CMS data is added to the CT14HERA2 global PDF fit, due to the larger impact of the inclusive jet data from both the Tevatron and the LHC. If the jet data are removed from the fit, then an impact is observed. If the CMS data is scaled by a larger weight, representing the greater statistical power of the jet data, a roughly equal impact on the gluon distribution is observed for the $t\overline{t}$ as for the inclusive jet data. For data samples with higher integrated luminosity at 13 TeV, a more significant impact of the double-differential $t\overline{t}$ data may be observed. (paper)