The small-x gluon from forward charm production: implications for a 100 TeV proton collider

We review the constraints on the small-x gluon PDF that can be derived by exploiting the forward D meson production data from the LHCb experiment at $\sqrt{s}=5,7$ and 13 TeV. We then discuss the phenomenological implications of the resulting improved small-x gluon for ultra-high energy astrophysics, in particular neutrino telescopes, as well as for the proposed Future Circular Collider (FCC) with $\sqrt{s}=100$ TeV. We illustrate how at the FCC even electroweak scale cross-sections can become sensitive to the small-x region of the quark and gluon PDFs, and then demonstrate how the addition of the LHCb heavy meson production measurements leads to a reduction of PDF uncertainties for various benchmark cross-sections.