Triggered by ongoing dark matter searches in the top quark sector at the Large Hadron Collider we report on the calculation of the next-to-leading order QCD corrections to the Standard Model process $ppto tbar{t}+ Z(to u_ell bar{ u}_ell)$. This calculation is based on matrix elements for $e^+ u_e , mu^- bar{ u}_mu , bbar{b} , u_tau bar{ u}_tau$ production and includes all non-resonant diagrams, interferences, and off-shell effects of the top quarks. Non-resonant and off-shell effects due to the finite $W$-boson width are also consistently taken into account. As it is common for such studies, we present results for both integrated and differential cross sections for a few renormalisation and factorisation scale choices and three different parton distribution functions. Already with the fairly inclusive cut selection and independently of the scale choice and the parton distribution function non-flat differential ${cal K}$-factors are obtained for $p_T^{miss}, Delta phi_{ellell}, Delta y_{ellell}, costheta_{ellell}, H_T, H^prime_T$ observables that are relevant for new physics searches. Good theoretical control over the Standard Model background is a fundamental prerequisite for a correct interpretation of possible signals of new physics that may arise in this channel. Thus, these observables need to be carefully reexamined in the presence of more exclusive cuts before any realistic strategies for the detection of new physics signal can be further developed.
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