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.
Effects of vacuum polarization by hadronic and heavy-fermion insertions were the last unknown two-loop QED corrections to high-energy Bhabha scattering and have been first announced in cite{Actis:2007fs}. Here we describe the corrections in detail an
d explore their numerical influence. The hadronic contributions to the virtual O(alpha^2) QED corrections to the Bhabha-scattering cross-section are evaluated using dispersion relations and computing the convolution of hadronic data with perturbatively calculated kernel functions. The technique of dispersion integrals is also employed to derive the virtual O(alpha^2) corrections generated by muon-, tau- and top-quark loops in the small electron-mass limit for arbitrary values of the internal-fermion masses. At a meson factory with 1 GeV center-of-mass energy the complete effect of hadronic and heavy-fermion corrections amounts to less than 0.5 per mille and reaches, at 10 GeV, up to about 2 per mille. At the Z resonance it amounts to 2.3 per mille at 3 degrees; overall, hadronic corrections are less than 4 per mille. For ILC energies (500 GeV or above), the combined effect of hadrons and heavy-fermions becomes 6 per mille at 3 degrees; hadrons contribute less than 20 per mille in the whole angular region.
Using dispersion relations, we derive the complete virtual QED contributions to Bhabha scattering due to vacuum polarization effects in photon propagation. We apply our result to hadronic corrections and to heavy lepton and top quark loop insertions.
We give the first complete estimate of their net numerical effects for both small and large angle scattering at typical beam energies of meson factories, LEP, and the ILC. The effects turn out to be smaller, in most cases, than those corresponding to electron loop insertions, but stay, with amounts of typically one per mille, of relevance for precision experiments. Hadronic corrections themselves are typically about 2-3 times larger than those of intermediate muon pairs (the largest heavy leptonic terms).
