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We present the computation of the differential cross section for the process$pp(\bar{p}) \to (W^+\,W^-\,b\,\bar{b}\to)\;e^+\,\nu_e\,\mu^-\,\bar{\nu}_\mu\,b\, \bar{b}+X$ at NLO QCD accuracymatched to Shower Monte Carlo (SMC) simulations using PowHel, on the basis ofthe interface between HELAC-NLO and POWHEG-BOX. We include all resonant andnon-resonant contributions. This is achieved by fully taking into account theeffect of off-shell t-quarks and off-shell W-bosons in the complex mass scheme.We also present a program called DECAYER that can be used to let the t-quarkspresent in the event files for $pp(\bar{p}) \to {t\,\bar{t}\,X}$ processesdecay including both the finite width of the t-quarks and spin correlations. Wepresent predictions for both the Tevatron and the LHC, with emphasis ondifferences emerging from three different $W^+\,W^-\,b\,\bar{b}$hadroproduction computations: (i) full implementation of the $p\,p(\bar{p}) \toW^+\,W^-\,b\,\bar{b}$ process, (ii) generating on-shell t-quarks pushedoff-shell with a Breit-Wigner finite width and decayed by DECAYER, and (iii)on-shell t-quark production followed by decay in the narrow widthapproximation, as described by the SMC.

Hadroproduction of $W^+ W^- b \bar{b}$ at NLO accuracy matched with shower Monte Carlo programs