  We present a complete description of top quark pair production in association
with a jet in the dilepton channel. Our calculation is accurate to
next-to-leading order in QCD (NLO) and includes all non-resonant diagrams,
interferences and off-shell effects of the top quark. Moreover, non-resonant
and off-shell effects due to the finite W gauge boson width are taken into
account. This calculation constitutes the first fully realistic NLO computation
for top quark pair production with a final state jet in hadronic collisions.
Numerical results for differential distributions as well as total cross
sections are presented for the Large Hadron Collider (LHC) at 8 TeV. With our
inclusive cuts, NLO predictions reduce the unphysical scale dependence by more
than a factor of 3 and lower the total rate by about 13% compared to leading
order QCD (LO) predictions. In addition, the size of the top quark off-shell
effects is estimated to be below 2%.
