  We present a general formalism for the calculation of finite-width
contributions to the differential production cross sections of unstable
particles at hadron colliders. In this formalism, which employs an
effective-theory description of unstable-particle production and decay, the
matrix element computation is organized as a gauge-invariant expansion in
powers of $\Gamma_X/m_X$, with $\Gamma_X$ and $m_X$ the width and mass of the
unstable particle. This framework allows for a systematic inclusion of
off-shell and non-factorizable effects whilst at the same time keeping the
computational effort minimal compared to a full calculation in the complex-mass
scheme. As a proof-of-concept example, we give results for an NLO calculation
of top-antitop production in the $q \bar{q}$ partonic channel. As already found
in a similar calculation of single-top production, the finite-width effects are
small for the total cross section, as expected from the na\" ive counting $\sim
\Gamma_t/m_t \sim 1%$. However, they can be sizeable, in excess of 10%, close
to edges of certain kinematical distributions. The dependence of the results on
the mass renormalization scheme, and its implication for a precise extraction
of the top-quark mass, is also discussed.
