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We investigate a number of observables that are and will be instrumental inthe exploration of $\tbart$ production and decay at the Tevatron and the LHC.For this analysis we made a computer program that incorporates besides the NLOQCD corrections to $\tbart$ production and decay also mixed weak-QCDcorrections to the production amplitudes, and that allows for studies ofcorrelated versus uncorrelated $\tbart$ events. In this paper we analyze andcompute observables mostly for dileptonic $\tbart$ final states tonext-to-leading order in the strong and weak gauge couplings (NLOW), withselection cuts. We calculate charge asymmetries of the top quark and of$\ell=e,\mu$ and we compare, where possible, with experimental results. We showthat top-quark spin correlations affect a leptonic pair asymmetry (which hasnot been measured so far) by $\sim 7%$. We determine several dileptonic angularcorrelations, which reflect $\tbart$ spin correlations, namely the beam,off-diagonal and helicity correlation, and the opening angle distribution(defined in the $t$, $\bar t$ rest frames) when selection cuts are applied. OurNLOW predictions for the beam, off-diagonal, and helicity correlation for theTevatron agree with recent measurements by the CDF and D0 experiments. Inaddition we make predictions for estimators of these correlations as functionsof $\mtt$. These estimators may prove useful for the Tevatron and also in theearly rounds of LHC data-analyses, where the event numbers will probably not beabundant. Furthermore, we compute to NLOW in the gauge couplings two dileptonangular correlations that are defined in the laboratory frame, for correlatedand uncorrelated $\tbart$ events at the LHC. Finally, based on our SM results,we identify several observables that allow to search for non-standard parity-and CP-violating interactions, especially with future LHC data.

Distributions and correlations for top quark pair production and decay at the Tevatron and LHC.