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We report on our recent calculation for the off-shell $t\bar{t}b\bar{b}$process in the di-lepton decay channel at the LHC. Our results take intoaccount NLO QCD corrections for the complete $pp\to e^+\nu_e\mu^- \bar{\nu}_\mub\bar{b}b\bar{b}$ process, and include all double, single and non-resonantcontributions. We investigate the size of the corrections and their associatedtheoretical uncertainties. We also briefly comment on the impact of different$b$ jet definitions on our results.

off-shell $t\bar{t}b\bar{b}$ in the di-lepton channel