The total top quark pair production cross-section at hadron colliders through $\cal{O} (\alpha_{S}^{4})$

We compute the next-to-next-to-leading order (NNLO) QCD correction to the total cross-section for the reaction gg \to t\bar t + X. Together with the partonic channels we computed previously, the result derived in this letter completes the set of NNLO QCD corrections to the total top pair production cross-section at hadron colliders. Supplementing the fixed order results with soft-gluon resummation with next-to-next-to-leading logarithmic accuracy we estimate that the theoretical uncertainty of this observable due to unknown higher order corrections is about 3% at the LHC and 2.2% at the Tevatron. We observe a good agreement between the Standard Model predictions and the available experimental measurements. The very high theoretical precision of this observable allows a new level of scrutiny in parton distribution functions and new physics searches.