We discuss production of charm and bottom quarks at forward rapidity in pp collisions at the LHC, updating the QCD predictions for the run at sqrt{S}=13 TeV. We show that, while the absolute rates suffer from large theoretical systematics, dominated
by scale uncertainties, the increase relative to the rates precisely measured at 7 TeV can be predicted with an accuracy of a few percent, sufficient to highlight the sensitivity to the gluon distribution function.
Incorporating all recent theoretical advances, we resum soft-gluon corrections to the total $tbar t$ cross-section at hadron colliders at the next-to-next-to-leading logarithmic (NNLL) order. We perform the resummation in the well established framewo
rk of Mellin $N$-space resummation. We exhaustively study the sources of systematic uncertainty like renormalization and factorization scale variation, power suppressed effects and missing two- and higher-loop corrections. The inclusion of soft-gluon resummation at NNLL brings only a minor decrease in the perturbative uncertainty with respect to the NLL approximation, and a small shift in the central value, consistent with the quoted uncertainties. These numerical predictions agree with the currently available measurements from the Tevatron and LHC and have uncertainty of similar size. We conclude that significant improvements in the $tbar t$ cross-sections can potentially be expected only upon inclusion of the complete NNLO corrections.
